Crystallochemical Design of Huntite-Family Compounds

crystals

Review Crystallochemical Design of Huntite-Family Compounds

Galina M. Kuz’micheva 1, Irina A. Kaurova 1,* , Victor B. Rybakov 2 and Vadim V. Podbel’skiy 3 1 MIREA-Russian Technological University, Vernadskogo pr. 78, Moscow 119454, Russia; [email protected] 2 Lomonosov Moscow State University named M.V. Lomonosov, Vorobyovy Gory, Moscow 119992, Russia; [email protected] 3 National Research University Higher School of Economics, Myasnitskaya str. 20, Moscow 101000, Russia; [email protected] * Correspondence: [email protected]; Tel.: +7-495-246-0555 (ext. 434)

Received: 18 December 2018; Accepted: 12 February 2019; Published: 15 February 2019

Abstract: Huntite-family nominally-pure and activated/co-activated LnM3(BO3)4 (Ln = La–Lu, Y; M = Al, Fe, Cr, Ga, Sc) compounds and their-based solid solutions are promising materials for lasers, nonlinear optics, spintronics, and photonics, which are characterized by multifunctional properties depending on a composition and crystal structure. The purpose of the work is to establish stability regions for the rare-earth orthoborates in crystallochemical coordinates (sizes of Ln and M ions) based on their real compositions and space symmetry depending on thermodynamic, kinetic, and crystallochemical factors. The use of diffraction structural techniques to study single crystals with a detailed analysis of diffraction patterns, reﬁnement of crystallographic site occupancies (real composition), and determination of structure–composition correlations is the most efﬁcient and effective option to achieve the purpose. This approach is applied and shown primarily for the rare-earth scandium borates having interesting structural features compared with the other orthoborates. Visualization of structures allowed to establish features of formation of phases with different compositions, to classify and systematize huntite-family compounds using crystallochemical concepts (structure and superstructure, ordering and disordering, isostructural and isotype compounds) and phenomena (isomorphism, morphotropism, polymorphism, polytypism). Particular attention is paid to methods and conditions for crystal growth, affecting a crystal real composition and symmetry. A critical analysis of literature data made it possible to formulate unsolved problems in materials science of rare-earth orthoborates, mainly scandium borates, which are distinguished by an ability to form internal and substitutional (Ln and Sc atoms), unlimited and limited solid solutions depending on the geometric factor.

Keywords: huntite family; rare-earth scandium borate; optical material; crystal growth; rare-earth cations; X-ray diffraction (XRD); crystal structure; solid solution; order–disorder

1. Introduction Modern scientific and applied materials science requires both an appearance of new materials with a desired combination of functional properties and an improvement and optimization of physical parameters and structural quality of the known materials, which have already proven themselves in practice, with further control of their properties using external (growth and post-growth treatment conditions) or internal (activation, isomorphic substitution) effects. Isomorphic substitutions and activation are different in the concentration of ion(s) introduced into a crystal matrix and effects produced. Isomorphic substitution is a powerful and flexible way to obtain a desired physical parameter of material by a targeted change in the composition of specific crystal structure. Activation is one of the necessary and relatively simple technological actions for the appearance, modification, and improvement of crystal properties by introduction (sometimes, over stoichiometry) of small amounts

Crystals 2019, 9, 100; doi:10.3390/cryst9020100 www.mdpi.com/journal/crystals Crystals 2019, 9, 100 2 of 49 of impurity ions into a crystal matrix that contributes to a self-organization and self-compensation of system’s electroneutrality. It is possible that dopant ions introduced into a crystal structure in low concentrations over stoichiometry are distributed over crystallographic sites in a different way than those introduced in high concentrations in the case of formation of solid solutions. However, low content of dopant ions can lead to significant changes in both local and statistical structures, in particular, in crystal symmetry. In this paper, all the above-mentioned aspects are reviewed for the huntite family compounds, interesting and important materials from both applied and scientific points of view, with the main focus on single-crystal objects, a detailed study of which can obtainin reliable information about the internal structure of materials. Complex orthoborates of rare-earth metals with the general chemical formula LnM3(BO3)4, where 3+ 3+ Ln = La–Lu, Y and M = Al, Ga, Sc, Cr, Fe, belong to the huntite family (huntite CaMg3(CO3)4, space group R32 [1]). Depending on the composition and external conditions, they can have both monoclinic (space groups C2/c, Cc, and C2) and trigonal (space groups R32, P321, and P312) symmetry with the presence (space group C2/c) or absence of center of symmetry. The most widely known and studied representatives of the huntite family compounds are 3+ 3+ aluminum borates LnM3(BO3)4 with the M = Al. The LnAl3(BO3)4 crystals with the Ln = Y, Gd, Lu doped with the Nd, Dy, Er, Yb, Tm (for example, [2,3]) and co-doped with the Er/Tb, Er/Yb, Nd/Yb ions (for example, [4,5]), as well as single-crystal solid solutions in the YAl3(BO3)4 – NdAl3(BO3)4 system [6], are promising materials for self-frequency-doubled lasers. YAl3(BO3)4 crystals doped with the Er3+ or Yb3+ ions are widely used in medicine and telecommunications as laser materials 3+ with a wavelength of 1.5–1.6 µm [4,5]. The LnAl3(BO3)4 crystals with the Ln = Tb, Ho, Er, Tm exhibit a magnetoelectric effect (HoAl3(BO3)4 is a leader among these compounds) (for example, [2,7]). 3+ The LnAl3(BO3)4 compounds with the Ln = Gd, Eu, Tb, Ho, Pr, Sm are used as phosphors (for 3+ 3+ example, [8,9]): the YAl3(BO3)4 crystals doped with the Eu and Tb ions is an environmentally friendly material for a white LED, having high intensity and luminescence power and low cost [10]; those doped with the Tm3+ and Dy3+ are able to be tuned from blue through white and ultimately to yellow emission colors and are attractive candidates for general illumination [11]; those doped 3+ 3+ with the Sm ions, as well as GdAl3(BO3)4:Sm , can be used as promising materials for orange-red lasers [8]. The simultaneous generation of three basal red–green–blue colors is obtained from a lone 3+ GdAl3(BO3)4:Nd bi-functional laser and optical nonlinear crystal [12], which is also of interest for the development of high-quality and bright displays. 3+ Rare-earth gallium borates LnM3(BO3)4 with the M = Ga are poorly studied. The LnGa3(BO3)4 3+ 3+ crystals, in particular LnGa3(BO3)4:Tb with the Ln = Y or Gd, are prominent luminescent materials with plasma-discharge conditions, converting a vacuum ultraviolet radiation into a visible light that can be used in high-performance plasma display panels and television devices [13]. In addition, gallium borates can be considered as promising materials not only for luminescent and laser applications, but also for use in spintronics: a large magnetoelectric effect was found in the HoGa3(BO3)4 [14]. 3+ Rare-earth borates LnM3(BO3)4 with the magnetic ions M = Fe or Cr, which are characterized by the presence of two interacting magnetic subsystems (3d- and 4f - ions) in the crystal structure, are even less studied. A long-range antiferromagnetic spin order of the Cr3+ subsystem is observed in the NdCr3(BO3)4 single crystals at TN = 8 K [15]. A phase transition from paramagnetic to antiferromagnetic state was found in the EuCr3(BO3)4 crystals at TN ≈ 9 K [16]. In addition, a magnetic phase transition is also observed in the SmCr3(BO3)4 at Tc = 5 ± 1 K [17]. In a number of rare-earth ferroborates, a significant magnetoelectric effect was found [18,19], which makes it possible to attribute them to a new class of multiferroics [18]. Maximum magnetoelectric and magnetodielectric effects were recorded for the NdFe3(BO3)4 and SmFe3(BO3)4 crystals [19,20]. Such materials can be used as magnetoelectric sensors, memory elements, magnetic switches, spintronics devices, high-speed radiation-resistant MRAM memory, etc. 3+ Rare-earth scandium borates LnM3(BO3)4 with the M = Sc demonstrate an anomalously low luminescence concentration quenching, which is caused by the large distance between the nearest Crystals 2019, 9, 100 3 of 49

Ln ions (~6 Å), and, hence, these compounds are promising high-efficient optical media that can be used in photonics, in particular, to create a diode-pumped compact lasers covering various optical spectral regions [21,22]. Currently, the best materials for medium-power solid-state miniature lasers 3+ are undoped and Cr -doped NdSc3(BO3)4 [22,23]. They are characterized by a high efficiency of laser transitions, on the one hand, and detuning of almost all cross-relaxation transitions, on the other. In addition, the NdSc3(BO3)4 crystals have a high non-linear dielectric susceptibility. Hence, in these crystals, it is possible to convert an infrared radiation of the neodymium laser into a visible one along a certain crystal orientation relative to the propagation of laser radiation. A miniature laser emitted in a green spectral region can be created based on the NdSc3(BO3)4. As can be seen from the short literature review on properties and possible areas of application of the huntite-family borates, these materials are characterized by a combination of different functional properties in one compound. In turn, physical and chemical properties are due to a real composition and crystal structure, influenced by initial composition (the type of rare-earth metal and the nature of M metal), synthesis conditions, and external effects. Determination of structure of huntite-family rare-earth borates becomes very important, since a possible structural transition from one space group to another can be accompanied by a loss (or acquisition) of the center of symmetry and results in an acquisition (or loss) of nonlinear optical and magnetoelectric properties. Sardar et al. [24] found that the introduction of 5 at % Nd3+ ions 20 −3 (2.3 × 10 cm ; activation) into the LaSc3(BO3)4 crystal leads to a change in symmetry from the space group C2/c to C2, i.e., to a transition from a centrosymmetric to a non-centrosymmetric structure. In addition, it was shown that the introduction of Nd3+ ions in a concentration more than or equal to 50 at % to the LaSc3(BO3)4 crystal (solid solution) results in the space group transition from C2/c to R32 [25]. A comprehensive study of solid solutions in the system NdCr3(BO3)4 (sp. gr. C2/c)–GdCr3(BO3)4 (sp. gr. R32) using spectroscopic methods showed that the NdxGd1−xCr3(BO3)4 borates with x < 0.2 have essentially trigonal non-centrosymmetric structure (sp. gr. R32), and already in the case of 20% Nd concentration in the crystals, an additional large content of the monoclinic phase (sp. gr. C2/c) is observed [26]. Knowledge of a precise real composition of crystals is no less important. Bulk crystals, usually obtained by the most technological melt methods, can have a homogeneous composition only for compounds with the congruent melting (CM). However, an activation of crystal or a synthesis of mixed crystals (solid solutions) leads to a deviation of a real composition from the CM one. In addition, a real composition of grown crystal, taking into account compositions of all crystallographic sites, usually differ from that of initial charge (melt). However, in the overwhelming majority of cases, observed physical properties of materials are ‘attributed’ to initial charge composition that leads to incorrect conclusions about correlations in the fundamental triad ‘composition-structure-properties’. Thus, to improve properties of huntite-family single crystals and expand the scope of their application as well as to synthesize and create materials with a required combination of operating parameters, it is necessary to know a precise real crystal composition, structural effects, and crystallochemical limits of existence (stability limits) of a compound or solid solution with a specific symmetry. This is the motivating force for the research, the results of which are reported on here. Currently, various approaches are developed to avoid time-consuming searches for materials with a specific crystal structure and desired physical parameters and to optimize and simplify ways of their obtaining. One of the most effective techniques is a type of crystal engineering which is shown here for the huntite-family compounds. In this approach, the ‘composition-structure-property’ correlations for a specific class of materials as well as possible structural types with chemical element sets formed crystal structure, coordination environment of atoms in the structure, nature of chemical bond between different atomic groups, etc. are analyzed. When forecasting new structures or describing the known ones, it is necessary to take into account crystallochemical characteristics of atoms or ions in the structure, namely, a radius, an electronegativity, a formal charge, and hence a coordination number and bonds between the components. An approach described is one of the main driving forces in the applied Crystals 2019, 9, 100 4 of 49 crystallochemistry—a section of materials science, which combines knowledges from fundamental crystallochemistry and specialists in other scientific fields dealing with materials. One of the main tasks of applied crystallochemistry is an investigation of functional correlations of the form of P = P(X), where X is a material and P is a property. In this case, properties are considered depending on the crystallochemical individuality of the components in a number of related compounds. A computer design of such structures involves a generation of polyhedra, a search for possible packages with the following determination of all required structural parameters.

2. Materials and Methods In this review, single crystals are predominantly described and a preference is given to X-ray diffraction research techniques—a powerful tool to determine fundamental characteristics of an object, in particular, a real composition and structure, with a high degree of accuracy and reliability and to reasonably relate functional properties to a composition and structure depending on the prehistory of crystals (composition of initial charge, growth and post-growth treatment conditions). A crystallochemical approach based on the knowledge of basic laws of structure formation and correlations between real composition, structure, growth conditions, and physical properties of materials, makes it possible to optimize a search for new promising compounds and to improve functional properties of the known ones. The use of information technologies applied crystallochemical models for a subsequent creation of mathematical models and specialized programs on their basis accelerates a transition from theory to practice, and further to a technology to grow material with controlled properties. 3+ 3+ The LnM3(BO3)4 crystals, where Ln = La–Lu, Y, M = Al, Fe, Ga, Cr, melt incongruently and are usually obtained by the flux method from the high-temperature solutions both via spontaneous crystallization and using a seed, which is described in detail in [21,27–29]. The use of the flux method, as the most suitable for growing such crystals, has a significant drawback—an incorporation of flux components into the growing crystal. The K2Mo3O10–B2O3 mixed flux is usually applied to grow huntite-family borates [21,27,30], however, the Mo ions easily incorporate into a crystal, which leads to an appearance of a near ultraviolet absorption band that inhibits the use of these nonlinear optical crystals at short wavelength [21,27,31]. In addition, crystals have low growth rate and small sizes (1–20 mm), which leads to an impossibility of obtaining bulk samples of good optical quality suitable for further use. In [21,32,33] only, the relatively large LnM3(BO3)4 crystals, in particular, YAl3(BO3)4 and GdAl3(BO3)4, up to 45 mm in size have been synthesized by the top-seeded solution growth (TSSG) method. In addition, it should be noted that the polycrystalline gallium borates with the Ln = La, Nd, Sm, Gd, Ho, Y, Er, and Yb were sintered in Pt crucible in air atmosphere at T = 575–1050 ◦C from pellets made from Ln2O3, Ga2O3, and B2O3 oxide powders [34]. As a result, the dominant metaborate Ln(BO2)3 for the Ln = La and Nd, huntite LnGa3(BO3)4 for the Ln = Sm, Gd, Ho, Y and Er, the new dolomite YbGa(BO3)2, the intermediate LnBO3 and GaBO3 phases were identified by X-ray powder diffraction measurements. A significant advantage of the LnSc3(BO3)4 scandium borates is a possibility of synthesis of large-sized single crystals using the Czochralski technique (Ln = La, Ce, Pr, Nd; in particular, [35]). Wherein, the degree of congruence of LnSc3(BO3)4 decreases from La to Nd [35], and compounds with the Ln = Y and Gd melt incongruently [36,37]. Durmanov et al. [33] developed the modified heating assembly served to effectively control both the process of possible condensation of B2O3 vapors on the surface of the growing crystal and thermal gradients over the crucible and in the melt. It guaranteed synthesis of high-quality optical LaSc3(BO3)4 single crystals (both pure and doped with the Nd, Yb, Er/Yb, Er/Yb/Cr, Pr), CeSc3(BO3)4, PrSc3(BO3)4 (both pure and doped with the Nd), NdSc3(BO3)4, as well as solid solutions, in particular, those with the general chemical compositions (Ce,Nd)Sc3(BO3)4, (Ce,Gd)Sc3(BO3)4, (Nd,Gd)Sc3(BO3)4, (Ce,Nd,Gd)Sc3(BO3)4, (Ce,Y)Sc3(BO3)4, Ce(Lu,Sc)3(BO3)4, (Ce,Nd)(Lu,Sc)3(BO3)4. Crystals 2019, 9, 100 5 of 49

Single crystals with the general composition LnSc3(BO3)4 (Ln = La, Ce, Pr, Nd, Tb), in particular, with the initial charge compositions LaSc3(BO3)4, CeSc3(BO3)4, Pr1.1Sc2.9(BO3)4, Pr1.25Sc2.75(BO3)4, NdSc3(BO3)4, Nd1.25Sc2.75(BO3)4, TbSc3(BO3)4 and single-crystal solid solutions with the initial compositions (La,Nd)Sc3(BO3)4, (Ce,Nd)1+xSc3−x(BO3)4, (La,Pr)Sc3(BO3)4, La(Sc,Yb)Sc3(BO3)4, La(Sc,Er)Sc3(BO3)4, La(Sc,Er,Yb)Sc3(BO3)4, (Ce,Gd)Sc3(BO3)4, (Ce,Gd)1+xSc3−x(BO3)4, (Nd,Gd)1+xSc3−x(BO3)4, (Ce,Nd,Gd)Sc3(BO3)4, (Ce,Y)1+xSc3−x(BO3)4, (Ce,Lu)1+xSc3−x(BO3)4, (Ce,Nd,Gd)1+xSc3−x(BO3)4 (Ce,Nd,Lu)1+xSc3−x(BO3)4, described in this work, having averaged diameter of 15–25 mm and length of 30–150 mm were grown by the Czochralski technique in Ir crucibles at pulling rate 1–3 mm/h and seed rotation 8–12 rpm. An Ir rod of 2 mm in diameter was initially used as a seed. Oriented single-crystal seeds were cut from the crystals grown on the Ir rod. The seed was oriented so that its optical axis coincided with the pulling axis (within a few degrees). The methodology for Czochralski growth technique used to synthesis LnSc3(BO3)4 crystals (Ln = La, Ce, Pr, Nd, Tb) as well as single-crystal solid solutions is given in [38,39]. 3+ According to the literature data, a crystallization of LnM3(BO3)4 compounds (Ln = La–Lu, Y; M3+ = Al, Fe, Ga, Cr) in a specific space group was found using different techniques, namely, diffraction methods (D), infrared spectroscopy (IR), absorption spectroscopy (AS), transmission spectroscopy (TS), Raman spectroscopy (R); in addition, temperatures of structural phase transitions between forms with different space groups were determined using specific heat measurements (SH) and differential thermal analysis (DTA)[1,15,16,26,27,34–37,40–89] (Table1). In several works [ 36,49], the structures of the compounds were declared solely on the basis of a comparison of the experimental diffraction patterns with those given in the structural databases without any detailed structural analysis. In the overwhelming number of cases, the crystal structures (first of all, coordinates of atoms) of the samples were refined by the full-profile Rietveld method on polycrystalline samples obtained by the solid-state reaction (LnFe3(BO3)4 with the Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, (Y), Ho; LnGa3(BO3)4 with the Ln = Sm, Gd, Y, Ho, Er) [34,53] or on single crystals synthesized by the flux method and ground to a powder (LnAl3(BO3)4 with the Ln = Nd, Sm, Eu, Gd, Tb, Dy, (Y), Ho, Er, Yb; LnFe3(BO3)4 with the Ln = Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, (Y), Ho; LnGa3(BO3)4 with the Ln = Gd) [1,54,56,59,61,66,68]. Assignment of a series of rare-earth orthoborates (LnAl3(BO3)4 with the Ln = Nd, Eu, Gd, Tb, Dy, (Y), Ho, Er, Tm, Yb; LnFe3(BO3)4 with the Ln = Eu, Gd, Y; LnCr3(BO3)4 with the Ln = Sm, Eu, Gd, Tb, Dy; LnGa3(BO3)4 with the Ln = Nd, Eu, Gd, (Y), Ho) to the space group R32 is performed on powdered single crystals obtained by the flux method using IR spectroscopy coupled with the group-theoretical analysis [26,42,45,51,70,71,73], temperature-dependent high-resolution optical absorption Fourier spectroscopy and Raman spectroscopy (LnFe3(BO3)4 with the Ln = Pr, Nd) [57,58,60]. Crystal structures of single crystals were refined within the framework of the huntite structure (space group R32) for the LnAl3(BO3)4 (Ln = Nd, Sm, Eu, Gd, (Y), Tm, Yb), LnFe3(BO3)4 (Ln = La, Nd, Eu, Gd, Er), LnGa3(BO3)4 (Ln = Nd, Eu, Ho), LnSc3(BO3)4 (Ln = La, Ce, Pr, Nd, Sm, Eu) by the X-ray diffraction (XRD) analysis (Table1). It should be noted that in some literature sources (in particular, in [27]) it was not indicated on which samples, single-crystal or polycrystalline, a structural analysis has been performed; in [15,36,37,80], any methodology of structural studies is absent, the method of investigation, X-ray diffraction, being indicated only. Neutron diffraction study performed on powdered samples with the initial compositions YAl3(BO3)4,Y0.88Er0.12Al3(BO3)4,Y0.5Er0.5Al3(BO3)4, Y0.5Yb0.5Al3(BO3)4, and Y0.84Er0.01Yb0.15Al3(BO3)4, grown by the topseeded high temperature solution method, crystallized in the space group R32 [90]. Due to the fact that the neutron scattering amplitudes both for Er (b = 7.79 fm) and for Yb (b = 12.433 fm) are much greater than that for Al (b = 3.449 fm), according to the Rietveld calculations, it can be stated that the Er3+ and Yb3+ ions occupy the Y3+ sites. For the above-mentioned compounds, positional parameters have been refined only [90]. Crystals 2019, 9, 100 6 of 49

3+ Table 1. Space groups for the compounds with the general composition LnM3(BO3)4 with the M = Al, Fe, Cr, Ga, Sc (according to the literature data).

1 Space groups for the LnM3(BO3)4 Ln M = Al M = Fe M = Cr 2 M = Ga M = Sc R32: D/S [74,75] R32: D/? [27], D/P [53,54], C2/c: IR/S (70:30, 1040–1050 ◦C) [70], La Orthorombic symmetry: D/P [40] C2/c: D/S (or C2)[76], D/S [77], D/P [78] D/S [55] IR/S (1.5:1; 2.3:1) [71] Cc: D/S [79] R32: ?[80], D/S [81] C2/c: D/S [35,77,82–87] Ce R32: D/P [53] Refined composition: CeSc3(BO3)4 [82] R32: ?[80], D/S [88] C2/c (or C2): D/S [35,83] R32: D/? [27] R32: D/? [27], D/P [53], C2/c: IR/S (50:50, 900–950 ◦C; 70:30, ◦ P321: D/S (40% reflections R32)[82] Pr C2/c: D/? [27], D/S [41], IR/P [42] D/P (1.5, 300 K) [56], 1040–1050 C) [70], Refined compositions: C2: D/? [27] AS/S [57,58] IR/S (1:1; 1.5:1; 2.3:1) [71] (Pr0.919Sc0.081(4))Sc3(BO3)4 [82], (Pr0.924Sc0.076(4))Sc3(BO3)4 [82] R32: ?[80], D/S [77], D/S [88] R32: D/P [1], D/? [27], R32: D/? [27], ? [15] R32: D/? [27], D/P [53,54,59], D/S [55], P321 (or P3): D/S [86,87,89] D/S [43,44], IR/P [42,45] C2/c: IR/S (50:50, 900–950 ◦C; 70:30, R/S [60], R32: D/S [47], D/? [27], P321: D/S (40% reflections R32)[82] Nd C2/c: D/S [46,47], IR/P [42,45], 1040–1050 ◦C) [70], AS/S [57,58] IR/P [45] Refined compositions: D/P [48], ? [49] IR/S (1:1; 2.3:1) [71], C2/c: IR/P [45] C2: D/P [48], ? [49] IR/S [26,45] NdSc3(BO3)4 [82,89], (Nd0.910Sc0.090(20))Sc3(BO3)4 [82] R32: D/? [27], IR/S (1:1) [71], IR/S (50:50, 900–950 ◦C) [70] R32: D/P [1], D/? [27], D/S [50] C2/c: IR/S (70:30, 1040–1050 ◦C) [70], R32: D/? [27], Sm R32: D/? [27], D/P [53,54,61] R32: ?[80], D/S [88] C2/c: D/? [27], IR/P [42] IR/S [72] D/P [34] R32 + C2/c fragments: IR/S (1.5:1) [71] C2/c + R32: IR/S (2.3:1) [71] R32: D/? [27], D/S [62], D/P [53,54], R32: D/P [1], D/? [27], R32: D/? [27], D/P [16] IR/P [51] D/S [50], IR/S (50:50, 900–950 ◦C; 70:30, R32 (HT) and P3 21 (LT): SH/S, R32: D/? [27], D/S [73], Eu IR/P [42,51] 1 1040–1050 ◦C) [70], R32: D/S [88] T = 88 K [53]; IR/P [51,73] C2/c: D/? [27] s IR/S (1:1; 2.3:1) [71], AS/S, T = 58 K [57,58]; C2: D/S [41] s IR/S [51] TS/S, Ts = 84 K [62] R32: D/? [27], D/P [34,54], D/S (297 K) [63], IR/P [45], R32: D/P [1], D/? [27], R32: D/P [1], D/? [27], P3 21: D/S (90 K) [63] 1 IR/S (50:50, 900–950 ◦C; 70:30, R32: D/? [27], D/P [34,54], Gd D/S [50], D/P [52], IR/P [42,45] R32 (HT) and P3 21 (LT): SH/S, R32: ?[36,37] 1 1040–1050 ◦C) [70], IR/P [45] C2: D/S [46,47] T = 174 K [53]; s IR/S (1:1; 1.5:1; 2.3:1) [71], IR/S [26,45] R/S, Ts = 155 K [60]; AS/S, Ts = 133–156 K [57,58,64]; IR/S, Ts = 143 K [65] Crystals 2019, 9, 100 7 of 49

Table 1. Cont.

1 Space groups for the LnM3(BO3)4 Ln M = Al M = Fe M = Cr 2 M = Ga M = Sc R32: D/? [27], D/P [53,54], D/P (200 K, 300 K) [66] R32: D/? [27], IR/S (50:50, 900–950 ◦C) P3 21: D/P (2, 30, 40, 100 K) [66] 1 [70] R3 or R3-Calcite-type structure: R32: D/P [1], R32 (HT) and P3 21 (LT) SH/S, 1 R32 + C2/c fragments: IR/S (1:1) [71] D/S [35,83] Tb D/? [27], IR/P [42] T = 241 K [53]; R32: D/? [27] s C2/c + R32 fragments: IR/S (1.5:1) [71] Reﬁned composition: C2/c: D/S [41] R/S, T = 198 K [60]; s C2/c: IR/S (70:30, 1040–1050 ◦C) [70], AS/S, T = 198 K [57,58], (Tb0.25Sc0.75)BO3 [83] s IR/S (2.3:1) [71] Ts = 192 K [66]; IR/S, Ts = 200 K [65] R32: IR/S (50:50, 900–950 ◦C) [70], R32: D/? [27], D/P [53,54], IR/S (1.5:1) [71] P3 21: D/P (1.5, 50, 300 K) [67] Dy R32: D/P [1], D/? [27], IR/P [42] 1 R32 + C2/c fragments: IR/S (1:1) [71] R32: D/? [27] R32 (HT) and P3 21 (LT): SH/S, 1 C2/c: IR/S (70:30, 1040–1050 ◦C) [70], T = 340 K [53] s IR/S (2.3:1) [71] R32: D/? [27], D/P [53,54], IR/P [45], D/P (520 K) [68] R32: D/P [1], R32: D/? [27], P3 21: D/P (2, 50, 295 K) [68] (Y) D/S [46,47], 1 D/P [34], R32: ?[36,37] R32 (HT) and P3 21 (LT): DTA/S, D/? [27], IR/P [42,45] 1 IR/P [45] Ts = 445 K [53]; R/S, Ts = 350 K [60]; AS/S, Ts = 350 K [57,58] R32: D/? [27], D/P [53,54], R32: D/? [27] D/P (520 K) [68] R32: D/? [27], D/S [73], R32: D/P [1], D/? [27], IR/P [42] R32 + C2/c fragments: IR/S (1.5:1) [71], Ho P3 21: D/P (2, 50, 295 K) [68] D/P [34], C2/c: D/S [41] 1 C2/c: IR/S (70:30, 1040–1050 ◦C) [70], R32 (HT) and P3 21 (LT): DTA/S, IR/P [73] 1 IR/S (2.3:1) [71] Ts = 427 K [53] R32: D/? [27], D/S [69] P3 21: D/P (1.5, 300 K) [56] 1 R32: D/? [27], Er R32: D/P [1], D/? [27], IR/P [42] R32 (HT) and P3 21 (LT): R/S, T = 340 R32 + C2/c fragments: IR/S (1:1) [71] 1 s D/P [34] K[60]; AS/S, Ts = 340 K [57,58] Tm R32: D/? [27], D/S [41], IR/P [42] R32: D/? [27] R32: D/? [27] R32: D/P [1], D/? [27], D/S [41], Yb R32: D/? [27] R32: D/? [27] R3-Dolomite type IR/P [42] structure: D/P [34] Lu R32: D/? [27] 1 P—powder sample, S—single crystal sample, D—diffraction techniques, IR—infrared spectroscopy, AS—absorption spectroscopy, TS—transmission spectroscopy, R—Raman spectroscopy, SH—speciﬁc heat measurements, DTA—differential thermal analysis, HT—high-temperature phase, LT—low-temperature phase, Ts—phase transition temperature; A question mark (?) indicates a lack of data on the type of material under investigation or/and applied technique in the literature source. 2 The borate:solvent ratios in the batch and the temperature ranges are given in parentheses. Crystals 2019, 9, 100 8 of 49

Resuts of XRD study of the Czochralski-grown single crystals and solid solutions (“Enraf-Nonius” CAD-4 single-crystal diffractometer; room temperature; AgKα, MoKα or CuKα; size, ~ 0.1 × 0.1 × 3 0.1 mm ) with the initial compositions LaSc3(BO3)4, CeSc3(BO3)4, Pr1.1Sc2.9(BO3)4, Pr1.25Sc2.75(BO3)4, NdSc3(BO3)4, Nd1.25Sc2.75(BO3)4, TbSc3(BO3)4 and (La,Nd)Sc3(BO3)4, (Ce,Nd)1+xSc3−x(BO3)4, (La,Pr)Sc3(BO3)4, La(Sc,Yb)Sc3(BO3)4, La(Sc,Er)Sc3(BO3)4, La(Sc,Er,Yb)Sc3(BO3)4, (Ce,Gd)Sc3(BO3)4, (Ce,Gd)1+xSc3−x(BO3)4, (Nd,Gd)1+xSc3−x(BO3)4, (Ce,Nd,Gd)Sc3(BO3)4, (Ce,Y)1+xSc3−x(BO3)4, (Ce,Lu)1+xSc3−x(BO3)4, (Ce,Nd,Gd)1+xSc3−x(BO3)4 (Ce,Nd,Lu)1+xSc3−x(BO3)4, performed by our scientific group, are given in [35,76,82,83,85,89,91] and [35,84,86,87,91], respectively, and in the present work. To reduce an error associated with an absorption, the XRD data were collected over the entire Ewald sphere. The unit cell parameters are determined by an auto-indexing of the most intense 25 reflections. Furthermore, a detailed analysis of diffraction reflections, including low-intensity ones, was carried out to find a possible superstructure either with the multiple-increased unit cell parameters and another symmetry or with another symmetry only. In the case of a small number of reflections that do not obey the extinction rules of the chosen space group, these reflections were not taken into account when refining a crystal structure. In case of a large number of ‘forbidden’ reflections, a crystal structure was solved by direct methods or/and the Paterson method taking into account all diffraction reflections. The preliminary XRD data processing was carried out using the WinGX pack [92] with a correction for absorption. The atomic coordinates, anisotropic displacement parametersCrystals 2019, 9of FOR all PEER atoms, REVIEW and occupancies of all the sites (except for the B and O ones) were refined10 using the SHELXL2013 software package [93], taking into account the atomic scattering curves for neutral atoms. The structural parameters were refined in several steps: initially, the coordinates of ‘heavy’ atoms (Ln and Sc), and then those of ‘light’ atoms (O and then B) were refined together R32 with the atom displacement parameters in isotropic and then anisotropic C2/ approximations;c finally, the Lu C2 occupancies of the Ln and Scsites were refined step by step. Cc Yb P321 In theTm review, for the visualization and comparison of crystal structures P321* (ball-and-stick and P3 21 - Low-temperature phase polyhedral models)Er and individual polyhedra as well as for the calculation1 of structural parameters R32 + C2/c fragments (all interatomicHo distances, bond angles, etc.) of the huntite-family compounds C2/c + R32 fragments and solid solutions R3 Calcite-type structure with different(Y) symmetry, the improved and augmented computer program for the investigation Dy R3 Dolomite-type structure of the dynamics of changes in structural parameters of compounds with Orthorombic different symmetry symmetry has Tb been applied [94]. Theoretical diffraction patterns have been created using the DIAMOND [95] and Ln Gd specialized softwareEu developed for diffraction pattern indexing taking into account a selection of backgroundSm level for rhombohedral and hexagonal cells of the huntite structure and a refinement of unit cell parametersNd using different sets of diffraction reflections: CPU, Intel core i3; RAM, at least 4 GB; Code, C#; OS:Pr Windows 7 with the installed Microsoft.NET Framework 4.0 or higher; Size: 32 768 b. Ce

3. Results La Al Fe Cr Ga Sc 3.1. LnM (BO ) (M = Al, Fe, Cr, Ga, Sc) Compounds 3 3 4 M3+ All the known literature data on symmetry of the huntite-family compounds, determined mainly by diffraction and spectroscopic methods on both polycrystalline and single-crystal samples, are systematizedFigure 1. Space and given groups in for Table the 1compounds and Figure with1. It the can general be noted composition that almost LnM3 all(BO compounds3)4 with the M having3+ = 3+ the generalAl, Fe, Cr, composition Ga, Sc (accordingLnM3 (BOto the3) literature4 with the dataM given= Al, in Fe,Table Cr, 1). Ga, Sc have a modiﬁcation with the huntite structure (space group R32). The situation looks different if only the results of X-ray study of single crystals are taken into 3+3+ account (Figure(Figure2 2):): the the compounds compounds with with the the general general composition compositionLnM LnM3(BO3(BO33))44 withwith thethe MM = Al и Sc are most fully represented; aa modiﬁcationmodification withwith thethe huntitehuntite structurestructure (space(space groupgroupR R32)32) prevails.prevails.

R32 C2/c Lu C2

Yb Cc Tm P321 Er P 321* P3 21 - Low-temperature phase Ho 1 R3 Calcite-type structure (Y) Dy

Ln Gd

Eu Sm

Nd Pr Ce La Al Fe Cr Ga Sc M3+

Figure 2. Space groups for the single crystals with the general composition LnM3(BO3)4 with the M3+ = Al, Fe, Ga, Sc (according to the literature data on X-ray diffraction experiments given in Table 1).

In the crystal structure of the huntite CaMg3(CO3)4 (space group R32, a = 9.5027(6), c = 7.8212(6) Å, Z = 3) (Figure 3), the Ca2+ ion (rCaVI = 1.00 Å according to the Shannon system [96]) is located in the

Crystals 2019, 9 FOR PEER REVIEW 10

R32 C2/c Lu C2 Cc Yb P321 CrystalsCrystals2019, 20199, 100, 9Tm FOR PEER REVIEW P321* 10 9 of 49 P3 21 - Low-temperature phase Er 1 R32 + C2/c fragments Ho C2/c + R32 fragments R3 Calcite-type structure (Y) R3 Dolomite-type structure Dy OrthorombicR32 symmetry Tb C2/c Lu C2 Ln Gd Cc Yb P321 Eu Tm P321* Sm P3 21 - Low-temperature phase Er 1 R32 + C2/c fragments Nd HoPr C2/c + R32 fragments R3 Calcite-type structure (Y) Ce R3 Dolomite-type structure

DyLa Orthorombic symmetry Tb

Ln Gd Al Fe Cr Ga Sc Eu 3+

Sm M

Nd Pr

Ce 3 3 4 3+ Figure 1. Space groups for the compounds with the general composition LnM (BO ) with the M = Al, Fe, Cr,La Ga, Sc (according to the literature data given in Table 1). Al Fe Cr Ga Sc The situation looks different if only the results of X-ray study of single crystals are taken into M3+ account (Figure 2): the compounds with the general composition LnM3(BO3)4 with the M3+ = Al и Sc are most fully represented; a modification with the huntite structure (space group R32) prevails. Figure 1. Space groups for the compounds with the general composition LnM3(BO3)4 with the M3+ = Al, Fe, Cr, Ga, Sc (according to the literature data given in Table1). Figure 1. Space groups for the compounds with the general composition LnM3(BO3)4 with the M3+ = Al, Fe, Cr, Ga, Sc (according to the literature data given in Table 1). R32 The situation looks different if only the results of X-ray study C2/c of single crystals are taken into Lu C2 3+ account (FigureYb 2): the compounds with the general composition Cc LnM3(BO3)4 with the M = Al и Sc are most fully representedTm ; a modification with the huntite structure P321 (space group R32) prevails. Er P 321* P3 21 - Low-temperature phase Ho 1 R3 Calcite-type structure (Y) Dy R32 C2/c Tb Lu C2 Ln YbGd Eu Cc Tm P 321 Sm Er P 321* Nd P3 21 - Low-temperature phase Ho 1 Pr R3 Calcite-type structure (Y) Ce Dy La Tb

Ln Gd Al Fe Cr Ga Sc Eu 3+ Sm M

Nd Figure 2. SpacePr groups for the single crystals with the general composition LnM3(BO3)4 with the 3+ M = Al, Fe, Ga,Ce Sc (according to the literature data on X-ray diffraction experiments given in3+ Table1). Figure 2. Space groups for the single crystals with the general composition LnM3(BO3)4 with the M = Al, Fe, Ga, ScLa (according to the literature data on X-ray diffraction experiments given in Table 1). In the crystal structure of the huntite CaMg3(CO3)4 (space group R32, a = 9.5027(6), c = 7.8212(6) Å, 2+Al VI Fe Cr Ga Sc Z = 3) (FigureIn the3 crystal), the Ca structureion of (r Cathe huntite= 1.00 CaMg Å according3(CO3)4 (space to the group Shannon R32, systema = 9.5027(6), [96]) c is = located7.8212(6) in the M3+ centerÅ, ofZ = a 3) distorted (Figure 3), prism the Ca with2+ ion the(rCaVI CN = 1.00 Ca Å = according 6 (CN, coordination to the Shannon number). system [96]) The is located upper in triangular the face of prism is rotated with respect to the lower one by an angle ϕ = 9.596◦ (ϕ = 0◦ in the regular

2+ VI trigonal prism), the Ca–O interatomic distances being the same. The Mg ion (rMg = 0.72 Å) Figure 2. Space groups for the single crystals with the general composition LnM3(BO3)4 with the M3+ = is locatedAl, in Fe, the Ga, center Sc (according of a distorted to the literature octahedron data on X- withray diffraction three different experiments Mg–O given in interatomic Table 1). distances (CN Mg = 2 + 2 + 2). Crystallochemically-different B1 and B2 ions occupy the centers of isosceles (CN B1 =In 1 the + 2) crystal and equilateralstructure of (CNthe huntite B2 = 3)CaMg triangles,3(CO3)4 respectively.(space group R The32, a MgO = 9.5027(6),6 octahedra c = 7.8212(6) are joined 2+ VI by theÅ, edgesZ = 3) (Figure and form 3), the twisted Ca ion chains (rCa = extended 1.00 Å according parallel to to the the Shannonc axis (thesystem 31 [9axis).6]) is Thelocated B2 in atoms the are located at the two-fold axes in triangles between the chains from the MgO6 octahedra, forming a ‘spiral staircase’ around the 32 axes. Different chains are connected by the CaO6 trigonal prisms and BO3 triangles, where each individual CaO6 and BO3 group connects three chains [55,65]. Figure3 shows the XY and XZ projections of huntite-type unit cell of LnM3(BO3)4 (space group R32) as a Crystals 2019, 9, 100 10 of 49 ball-and-stick model (Figure3a,b) and polyhedra (Figure3c,d) as well as fragments of the structure, including the main coordination polyhedra (Figure3e,f), and individual coordination polyhedra for all crystallochemically-differentCrystals 2019, 9 FOR PEER atoms REVIEW in the crystal structure (Figure3g–i). 12

(a) (b)

X Y

(e) (f)

(g) (h) (i)

Figure 3. The unit cell of the LnM3(BO3)4 structure (space group R32) projected onto the (a) XY and (b) XZ planes; Combination of the coordination polyhedra projected onto the (c) XY and (d) XZ planes; Combination of selected coordination polyhedra projected onto the (e) XY and (f) XZ planes; Coordination polyhedra for the (g) Ln,(h) M,(i) B1 and B2. Crystals 2019, 9, 100 11 of 49

2+ 2+ 4− 3+ 3+ 3− A topological correspondence of the Ca Mg 3(CO3) 4 and Ln M 3(BO3) 4 formulas, a similar coordination environment of the C4+ and B3+ ions, a possibility of the compensation of system electroneutrality, and a presence of the Ca2+ and Ln3+, Mg2+ and Sc3+, Mg2+ and M3+ = Al, Ga, Fe ions in 2+ 2+ 4− the Goldschmidt–Fersman diagonal series should lead to the isostructurality of the Ca Mg 3(CO3) 4 3+ 3+ 3− and Ln M 3(BO3) 4 compounds (more precisely, these compounds are isotype, as evidenced by the lack of similarity in structures, typical of isostructural compounds [91]) despite the fundamental difference in the crystallochemical properties (dimensions, electronegativity values, formal charges). 3+ It should be noted that the Cr ions are surrounded by six O atoms, forming the regular CrO6 octahedra (CN Cr = 6) in the crystal structures of oxides due to the electronic structure (non-binding 3 configuration is symmetric to the octahedral field of ligands - dε ), unlike distorted MO6 octahedra in 2+ 2+ 4− 3+ 3+ 3− the huntite structure (another example confirmed that the Ca Mg 3(CO3) 4 and Ln Cr 3(BO3) 4 3+ 3+ 3− 3+ compounds are isotype). Hence, in the structure of the activated La Sc 3(BO3) 4:Cr crystal, the 3+ symmetry of the ScO6 polyhedra, which include Cr ions, as well as that of the whole crystal changes. 3+ 3+ 3− 3+ 3+ 3− This is confirmed by the XRD analysis of the La Sc 3(BO3) 4 and La Sc 3(BO3) 4:Cr single crystals, grown by the Czochralski method, with the monoclinic (space group C2/c) and triclinic (space group P1 or P1) symmetry, respectively [76]. In the latter case, quite a lot of reflections with the I < 3σ(I) are not indexed in the monoclinic syngony, and taking into account these reflections, the refined unit cell parameters of the LaSc3(BO3)4:Cr were found to be a = 7.7356(4), b = 9.8533(8), ◦ c = 12.0606(8) Å, α = 89.981(6), β = 105.437(5), γ = 90.045(6) , in contrast to those of the LaSc3(BO3)4, a = 7.727(1), b = 9.840(1), c = 12.046(3) Å, β = 105.42(2)◦. In the CaCO3-MgCO3 system, the CaCO3 (a ≈ 4.99, c ≈ 17.08 Å; space group R3c, Z = 6) and CaMg(CO3)2 (a ≈ 4.80, c ≈ 16.00 Å; space group R3, Z = 3) compounds with calcite and dolomite structures, respectively, are known. The Ca2+ and Mg2+ ions occupy regular and distorted octahedral sites in the calcite and dolomite structures, respectively, with an ordered arrangement of the Ca2+ and Mg2+ ions along the 3-fold axis, which leads to a decrease in the symmetry of CaMg(CO3)2 compared to the CaCO3. Based on the transformed compositions (CaCO3 ≡ Ca4(CO3)4, 3+ CaMg(CO3)2 ≡ Ca2Mg2(CO3)4) and addiction of Ln ions to predominantly trigonal-prismatic (Ln = La–Gd) or octahedral (Ln = Tb–Lu; as well as M3+ ions) coordination [35], it is possible that 3+ 3+ 3− compounds with the initial composition Ln M 3(BO3) 4 can have dolomite-like and calcite-like structures with an ordered arrangement of Ln3+ and M3+ ions over the octahedral sites both separately (full positional ordering) and jointly (partial positional ordering). This can be expected, 3+ 3+ 3− VI VI for example, for the Ln M 3(BO3) 4 with the Ln = Tm (rTm = 0.88 Å) or Yb (rYb = 0.87 Å) in 3+ VI VI combination with the M = Cr (rCr = 0.615 Å) or Ga (rGa = 0.620 Å), for which ∆rLn-M = ~0.25 Å, 3+ 3+ 3− forming the dolomite-type structure (∆rCa-Mg = 0.28 Å), and for the Ln M 3(BO3) 4 with the VI 3+ VI Ln = Tb (rTb = 0.92 Å) in combination with the M = Sc (rSc = 0.745 Å) (∆rTb-Sc = ~0.175 Å), forming the calcite-type structure. Indeed, a polycrystalline sample with the initial composition 3+ 3+ 3− ◦ Yb Ga 3(BO3) 4, which was sintered between 575 and 1050 C[34], and a single crystal with the 3+ 3+ 3− initial composition Tb Sc 3(BO3) 4, obtained by the Czochralski method [35,83], crystallize with a decrease in symmetry, but with the same unit cell parameters, forming superstructures to dolomite with the space group R3 (a = 4.726(3), c = 15.43(2) Å) and calcite with the space group R3 (a = 4.773(5), 3+ 3+ 3− c = 15.48(1) Å), respectively. The XRD analysis of Tb Sc 3(BO3) 4 single crystal allowed to reveal additional diffraction reflections hh0l with the h + l = 2n, which are absent for the space group R3c and possible for the space groups R3 and R3. For the crystals obtained, a non-synchronous second harmonic generation was not observed, which indicates the space groups R3. Single crystals with the initial composition LnSc3(BO3)4 with the Ln = La [74,75], Ce [81], Pr [80,88], Nd [77,80,88], Sm [80,88], Eu [88], obtained by the flux method (the NdSc3(BO3)4 were grown by the Czochralski method [77]), and also with the Ln = Gd [36,37] and Y [36,37], grown by the TSSG method, have a modification with the huntite structure (space group R32) (Figures1 and2). Fedorova et al. [ 78] as well as Li et al. [25] and Ye et al. [31] could not obtain a stable modification of LaSc3(BO3)4 with the space group R32 by solid state reaction (LaSc3(BO3)4 samples with the space group C2/c have been Crystals 2019, 9, 100 12 of 49 obtained) and by a high-temperature solution method, respectively, suggesting that this phase seems to be metastable or stable in a narrow temperature range. It should be noted that the space group R32 for the LnSc3(BO3)4 with the Ln = La [74,75], Ce [81], Pr [88], Nd [77,88], Sm [88], Eu [88] is determined by the single crystal XRD study, whereas for the Ln = Gd, (Y), the space group R32 is stated in [36,37] without any experimental confirmation, noting only that single crystals grown by the TSSG method exhibited well developed facets having the form of rhombohedral prisms characteristic of the space group R32. For the crystals grown by the Czochralski method from the initial charges with the compositions Pr1.1Sc2.9(BO3)4 (PSB–1.1) and Pr1.25Sc2.75(BO3)4 (PSB–1.25) (∆rPr−Sc = 0.245 Å), NdSc3(BO3)4 (NSB–1.0) and Nd1.25Sc2.75(BO3)4 (NSB–1.25) (∆rNd−Sc = 0.235 Å), a symmetry decrease from the space group R32 to P321 or P3 (Figures1 and2) was found by the XRD analysis (it should be noted that the value ∆rNd−Sc (Å) is less than the critical value ∆rLn−M = ~0.25 Å, at which the derivatives of the huntite structure are formed; ∆rPr−Sc (Å) is actually at the stability limit). The extinction laws for an overwhelming number of diffraction reflections witness a crystallization of these compounds in the space group R32. However, 60% of the additional reflections with the I ≥ 3σ(I) are described within the framework of the superstructure having the huntite unit cell parameters, but with the space group P321 or P3 (the structures were solved in the space group P321) with the h + k = 3n, l = 2n + 1 for hkl [82Crystals]. In crystal 2019, 9 structures FOR PEER REV withIEW the space group P321 (Figure4) compared with those with the space 14 group R32 (Figure3), the Ln and Sc crystallographic sites (Figure3a–f), are split into two (Figure4a–f), Ln1 and(FigureLn2 (Figure 4a–f), Ln4g),1 and sites Ln with2 (Figure a distorted 4g), sites trigonal-prismatic with a distorted oxygen trigonal environment-prismatic oxygen and two, environment Sc1 and Sc2and (Figure two, 4Sc1h), and sites Sc2 with (Figure a distorted 4h), sites octahedral with a distorted oxygenenvironment, octahedral oxygen respectively. environment, respectively.

X Y X

(a) (b) Z

X Y X

Z Figure 4. Cont. X X Y Y X

(e) (f)

Crystals 2019, 9 FOR PEER REVIEW 14

(Figure 4a–f), Ln1 and Ln2 (Figure 4g), sites with a distorted trigonal-prismatic oxygen environment and two, Sc1 and Sc2 (Figure 4h), sites with a distorted octahedral oxygen environment, respectively.

X Y X

(a) (b) Z

X Y X

Crystals 2019, 9, 100 13 of 49 (c) (d)

X X Y Y X

Crystals 2019, 9 FOR PEER REVIEW 15 (e) (f)

(g) (h) (i)

Figure 4. The unit cell of the PrSc3(BO3)4 (PSB–1.1 and PSB–1.25) structure (space group P321) Figure 4. The unit cell of the PrSc3(BO3)4 (PSB–1.1 and PSB–1.25) structure (space group P321) projected ontoprojected the (a) XY onto and the (b) ( XZa) XY planes; and (b Combination) XZ planes; Combination of the coordination of the coordination polyhedra projectedpolyhedra ontoprojected the ( c) XY onto the (c) XY and (d) XZ planes; Combination of selected coordination polyhedra projected onto and (d) XZ planes; Combination of selected coordination polyhedra projected onto the (e) XY and (f) the (e) XY and (f) XZ planes; Coordination polyhedra for the (g) Pr1 and Pr2, (h) Sc1 and Sc2, (i) XZ planes; Coordination polyhedra for the (g) Pr1 and Pr2, (h) Sc1 and Sc2, (i) B1–B4. B1–B4.

In addition,In addition, the numberthe number of B of crystallographic B crystallographic sites sites is alsois also increased increased in in the the structure structure with with the the space groupspaceP321 group (Figure P3214i) (Figure compared 4i) compared with the withR32 onethe (FigureR32 one3 i).(Figure A comparison 3i). A comparison of the XZ of projectionsthe XZ of theprojections structures of with the structures the space with groups the spaceR32 (Figuregroups R332b) (Figure and P321 3b) (Figureand P3214 b)(Figure indicates 4b) indicates an alternation an of layersalternation of atoms of layers La, Sc–B,of atoms O–La, La, Sc–B, Sc (Figure O–La, 3Scb) (Figure and La1, 3b) and Sc1–B, La1, O–La2, Sc1–B, O–La2, Sc2–B, Sc2–B, O (Figure O (Figure4b) and corresponding4b) and corresponding polyhedra polyhedra (Figure3d,f (Figures and Figure 3d,f and4d,f) Figures along 4d,f) the Zalong axis. the Z axis. The refined crystal compositions can be written as [(Pr0.419Sc0.081(4))(1)]Pr0.5(2)Sc3(BO3)4 The refined crystal compositions can be written as [(Pr0.419Sc0.081(4))(1)]Pr0.5(2)Sc3(BO3)4 ((Pr0.919Sc0.081(4))Sc3(BO3)4) (PSB–1.1) and [(Pr0.424Sc0.076(4))(1)]Pr0.5(2)Sc3(BO3)4 ((Pr0.924Sc0.076(4))Sc3(BO3)4) ((Pr0.919Sc0.081(4))Sc3(BO3)4) (PSB–1.1) and [(Pr0.424Sc0.076(4))(1)]Pr0.5(2)Sc3(BO3)4 ((Pr0.924Sc0.076(4))Sc3(BO3)4) (PSB–1.25)(PSB–1.25) [82], [ from82], from which which it follows it follows that that a symmetrya symmetry decrease decrease isis causedcaused by by the the distribution distribution of of(Pr, (Pr, Sc) Sc) “atoms” and Pr atoms over two trigonal-prismatic sites (partial positional ordering) (Figure 4). “atoms” and Pr atoms over two trigonal-prismatic sites (partial positional ordering) (Figure4) . Results of Results of the XRD analysis with a refinement of positional and atom displacement parameters of the XRD analysis with a refinement of positional and atom displacement parameters of single crystals single crystals with the initial composition PrSc3(BO3)4, obtained by the flux method, are given in with[88]. the initialOn the composition basis of systematic PrSc3 absences(BO3)4, obtainedhkil: -h + k by+ l ≠ the 3n and flux a method, successful are refinement given in of [88 the]. Ondata the for basis of systematiccrystal, the absences space grouphkil:- hwas+ k determined+ l 6= 3n and to abe successful R32; the refinementreal composition of the of data the forcrystal crystal, (i.e., the the space grouprefinement was determined of the site tooccupancies) be R32; the was real not composition determined [88]. of the crystal (i.e., the refinement of the site occupancies)Crystals was with not determinedthe initial compositions [88]. NdSc3(BO3)4 (NSB–1.0) and Nd1.25Sc2.75(BO3)4 (NSB–1.25) with the space group Р321 (in Figures 1,2, it is given as P321*) have the refined compositions Crystals with the initial compositions NdSc3(BO3)4 (NSB–1.0) and Nd1.25Sc2.75(BO3)4 (NSB–1.25) withNdSc the space3(BO3)4 group and (NdP3210.500(1)[Nd (in Figures0.410Sc0.090(20)1 and(2)]Sc2, it3(BO is3 given)4 ((Nd as0.910ScP0.090(20)321*))Sc have3(BO3 the)4), respectively. refined compositions These structures differ from each other (Figures 5,6) by an additional presence of the Sc ions in the NdSc3(BO3)4 and (Nd0.500(1)[Nd0.410Sc0.090(20)(2)]Sc3(BO3)4 ((Nd0.910Sc0.090(20))Sc3(BO3)4), respectively. trigonal-pyramidal Nd2 sites in the NSB–1.25 structure. It should be noted that the NSB structure is represented by right (NSB–1.0) (Figures 5a–f) and left (NSB–1.25) (Figire 6a–f) forms.

Crystals 2019, 9, 100 14 of 49

These structures differ from each other (Figures5 and6) by an additional presence of the Sc ions in the trigonal-pyramidal Nd2 sites in the NSB–1.25 structure. It should be noted that the NSB structure is Crystals 2019, 9 FOR PEER REVIEW 16 represented by right (NSB–1.0) (Figure5a–f) and left (NSB–1.25) (Figure6a–f) forms.

X Y X

(a) Z (b)

X X Y

Z X Y

(e) (f)

(g) (h) (i)

Figure 5. The unit cell of the NdSc3(BO3)4 (NSB–1.0) structure (space group P321) projected onto the Figure 5. The unit cell of the NdSc3(BO3)4 (NSB–1.0) structure (space group P321) projected onto the (a) XY(a and) XY (andb)XZ (b) planes;XZ planes; Combination Combination of of the the coordinationcoordination polyhedra polyhedra projected projected onto onto the ( thec) XY (c )and XY and (d) XZ planes; Combination of selected coordination polyhedra projected onto the (e) XY and (f) XZ (d) XZ planes; Combination of selected coordination polyhedra projected onto the (e) XY and (f) XZ planes; Coordination polyhedra for the (g) Nd1 and Nd2, (h) Sc1 and Sc2, (i) B1–B4. planes; Coordination polyhedra for the (g) Nd1 and Nd2, (h) Sc1 and Sc2, (i) B1–B4.

Crystals 2019, 9, 100 15 of 49 Crystals 2019, 9 FOR PEER REVIEW 17

Z X Y

(a) (b) Z

X Y X

(e) (f)

(g) (h) (i)

Figure 6. The unit cell of the NdSc3(BO3)4 (NSB–1.25) structure (space group P321) projected onto the Figure 6. The unit cell of the NdSc3(BO3)4 (NSB–1.25) structure (space group P321) projected onto the (a) XY( anda) XY ( band) XZ (b planes;) XZ planes; Combination Combination of of the the coordination coordination polyhedrapolyhedra projected projected onto onto the the (c) (XYc) XYandand (d) XZ planes; Combination of selected coordination polyhedra projected onto the (e) XY and (f) XZ (d) XZ planes; Combination of selected coordination polyhedra projected onto the (e) XY and (f) XZ planes; Coordination polyhedra for the (g) Nd1 and Nd2, (h) Sc1 and Sc2, (i) B1–B4. planes; Coordination polyhedra for the (g) Nd1 and Nd2, (h) Sc1 and Sc2, (i) B1–B4.

The NdO6 coordination polyhedra in the NSB–1.0 structure (Figure5g) are more distorted than those in the NSB–1.25 one (Figure6g), and the ScO 6 polyhedra in the NSB–1.0 structure (Figure5h) are more regular (especially the Sc1O6 polyhedron) than those in the NSB–1.25 one (Figure6h). It conﬁrms, Crystals 2019, 9 FOR PEER REVIEW 10

R32 C2/c Lu C2 Cc Yb P321 Tm P321* P3 21 - Low-temperature phase Er 1 Crystals 2019, 9 FOR PEER REVIEW R32 + C2/c fragments 18 Ho C2/c + R32 fragments R3 Calcite-type structure (Y) The NdO6 coordination polyhedra in the R3 NSB Dolomite-type–1.0 structure structure (Figure 5g) are more distorted than Dy Orthorombic symmetry Crystalsthose2019, 9in, 100 the NSB–1.25 one (Figure 6g), and the ScO6 polyhedra in the NSB–1.0 structure (Figure16 of 5h) 49 Tb 6 Ln Gd are more regular (especially the Sc1O polyhedron) than those in the NSB–1.25 one (Figure 6h). It

Eu confirms , firstly, a difference in their real compositions and, secondly, a ‘stress removal’ in the Sm ﬁrstly,NSB a difference–1.25 structure in their due real to compositionsthe presence of and, Sc atoms secondly, in trigonal a ‘stress-prismatic removal’ polyhedra. in the NSB–1.25 structure

Nd due to the Compared presence of to Sc the atoms PSB in structures trigonal-prismatic (Figure 4) polyhedra., in the NSB–1.0 structure (Figure 5), the ScO6 Pr Comparedcoordination to thepolyhedron PSB structures (Figures (Figure 4h, 5h)4), inand the one NSB–1.0 B polyhedron structure (Figures (Figure 4i,5), 5i) the are ScO less6 coordination distorted, as Ce polyhedron wel l as (Figures the  rotation 4h and 5angle h) and in onethe B Ln2O polyhedron6 coordination (Figures polyhedron4i and5i) areis smaller less distorted, (Figures as 4g, well 5g), as which the La ϕ rotationis caused angle by in the the presence Ln2O6 coordination of Sc atoms in polyhedron the Pr site isin smaller the PSB (Figures structures.4g and 5g), which is caused by Al the presence FeAs ofa result ScCr atoms of the in theanalysisGa Pr site of inFiguresSc the PSB 5 and structures. 6, it can be concluded that the crystals grown by the 3+ AsCzochralski a result M of method the analysis from of the Figures charges5 and 6 with, it can compositions be concluded NdSc that3(BO the3)4 crystals(NSB–1.0 grown) and by theNd Czochralski1.25Sc2.75(BO3)4 method(NSB–1.25 from) are characterized the charges by with the different compositions structure NdSc disordering3(BO3)4 (NSB–1.0)compared to and the Pr1.1Sc2.9(BO3)4 (PSB–1.1) and Pr1.25Sc2.75(BO3)4 (PSB–1.25); NSB and PSB are isotypic structures (space Nd1.25Sc2.75(BO3)4 (NSB–1.25) are characterized by the different structure disordering compared group P321) (Figures 4–6). The differences are related to a distribution of the Ln and Sc ions over the Figure 1. Space groupsto for the the Pr 1.1compoundsSc2.9(BO3 )with4 (PSB–1.1) the general and composition Pr1.25Sc2.75(BO LnM3)34(BO(PSB–1.25);3)4 with the NSB M3+ and= PSB are isotypic structures trigonal-prismatic sites, resulting in another type of structure, namely, unequal Nd1O6 and Nd2O6 Al, Fe, Cr, Ga, Sc (according(space to group the literatureP321) (Figures data given4–6 ).in The Table differences 1). are related to a distribution of the Ln and Sc ions over trigonal prisms in the NSB compared to the PSB structures and a different character of the changes in the trigonal-prismatic sites, resulting in another type of structure, namely, unequal Nd1O6 and Nd2O6 the interatomic distances in these polyhedra, primarily, the Nd(Pr)2–O4 и Nd(Pr)2–O1 ones [82]. The situation looks trigonaldifferent prisms if only in the the results NSB compared of X-ray tostudy the PSBof single structures crystals and are a different taken into character of the changes in The differences in the PSB–1.1, PSB–1.25, NSB–1.0, NSB–1.25 structures can be traced, for example, account (Figure 2): the compoundsthe interatomic with distances the general in thesecomposition polyhedra, LnM primarily,3(BO3)4 with the the Nd(Pr)2–O4 M3+ = Al и Nd(Pr)2–O1Sc ones [82]. The on their XZ projections (Figures 4b, 5b, 6b), paying attention to the B and O atoms. are most fully represented;differences a modification in the PSB–1.1, with the PSB–1.25, huntite structure NSB–1.0, (space NSB–1.25 group structures R32) prevails. can be traced, for example, on their Depending on the composition and growth conditions, the huntite-family compounds have XZ projections (Figures4b,5b and6b), paying attention to the B and O atoms. monoclinic modifications (Figures 1,2) with the centrosymmetric space group C2/c (Figure 7) and Dependingnon-centrosymmetric on the composition space groups and Cc (the growth extinction conditions, laws are the the huntite-family same as those for compounds the space group have monoclinic modifications (Figures1 and2) with the centrosymmetric space group C2/c (Figure7) and C2/c) (Figure 8) and C2 (Figure 9) R(the32 extinction laws are the same as those for the space groups non-centrosymmetricC2/m, Cm). space groups Cc (the C2/ extinctionc laws are the same as those for the space group C2/c) Lu (Figure8) and C2 (Figure9) (the extinction C2 laws are the same as those for the space groups C2/m, Cm).

Yb Cc Tm P321 Er P 321* P3 21 - Low-temperature phase Ho 1 R3 Calcite-type structure (Y) Dy

Ln Gd

Eu Sm

Nd Pr Ce (b) La (a) (c)

Al X Fe Cr Ga Sc 3+ Z M

(d) (e) (f)

Figure 7. Cont.

Crystals 2019, 9, 100 17 of 49 Crystals 2019, 9 FOR PEER REVIEW 19

X Z

(g) (h) (i)

(j) (k) (l)

FigureFigure 7. The 7. unitThe cellunit of cell the ofLnM the 3LnM(BO3(BO)4 structure3)4 structure (space (space group groupC2/ Cc)2/ projectedc) projected onto onto the the (a) ( XZ,a) XZ, (b )( XY,b) (c) YZXY, planes; (c) YZ planes; Combination Combination of the of coordination the coordination polyhedra polyhedra projected projected onto onto the the (d) ( XZ,d) XZ, (e) ( XY,e) XY, (f) ( YZf) planes;YZ Combinationplanes; Combination of selected of selected coordination coordination polyhedra polyhedra projected projected onto the onto (g) the XZ, (g (h) )XZ, XY, (h (i)) XY, YZ planes;(i) YZ Coordinationplanes; Coordination polyhedra polyhedra for the (j) Lnfor,( thek) (M1j) Lnand, (kM2) M1,( andl) B1 M2 and, (l B2.) B1 and B2.

The space group C2/c is known for the LnAl3(BO3)4 with the Ln = Pr, Nd, Sm, Eu, Tb, Ho (the structure is reﬁned, for example, in [97]); LnFe3(BO3)4 with the Ln = Nd; LnCr3(BO3)4 with the Ln = La, Pr, Nd, Sm, Tb, Dy, Ho; LnSc3(BO3)4 with the Ln = La, Ce, Pr (Table1). The centrosymmetry was determined by spectroscopic studies using a factor-group analysis of vibrations (for the LnAl3(BO3)4 with the Ln = Pr [42], Nd [42,45]; LnFe3(BO3)4 with the Ln = Nd [45]; LnCr3(BO3)4 with the Ln = La (Figure 10), Pr, Tb, Dy, Ho [70,71], Nd [26,45,70,71], Sm [70,72]). The LnSc3(BO3)4 crystals with the Ln = La, Ce, obtained by the Czochralski method, crystallize in the centrosymmetric space group C2/c), according to a study of their nonlinear optical properties [35]. The XRD investigation of the CeSc3(BO3)4 microcrystal with the space group C2/c indicates the similarity of charge and as-grown crystal compositions [82].

Crystals 2019, 9 FOR PEER REVIEW 20

Crystals 2019, 9, 100 18 of 49

X Y Y Z

X Z

(a) (b) (c)

(d) (e) (f)

Figure 8. Cont.

Crystals Crystals2019, 9, 2019 100 , 9 FOR PEER REVIEW 21 19 of 49

(g) (h) (i)

(j) (k) (l)

Figure 8. The unit cell of the LnM3(BO3)4 structure (space group Cc) projected onto the (a) XZ, (b) XY, (c) YZ planes; Combination of the coordination polyhedra Figure 8. The unit cell of the LnM3(BO3)4 structure (space group Cc) projected onto the (a) XZ, (b) XY, (c) YZ planes; Combination of the coordination polyhedra projectedprojected onto the onto (d )the XZ, (d) ( eXZ,) XY, (e) ( fXY,) YZ (f planes;) YZ planes; Combination Combination of selected of selected coordination coordination polyhedra polyhedra projected projected onto onto thethe ((gg)) XZ,XZ, ((hh)) XY,XY, ((ii) YZ planes; Coordination Coordination polyhedrapolyhedra for the for (j) theLn,( (jk) )LnM1–M3, (k) M1–M3,(l) B1–B4., (l) B1–B4.

Crystals 2019, 9 FOR PEER REVIEW 22 Crystals 2019, 9, 100 20 of 49

X Y Y Z

X Z

(a) (b) (c)

X Y Y

X Z

(d) (e) (f)

Figure 9. Cont.

Crystals 2019, 9, 100 21 of 49 Crystals 2019, 9 FOR PEER REVIEW 23

Y Y X

Z X Z

(g) (h) (i)

(j) (k) (l)

Figure 9. The unit cell of the LnM3(BO3)4 structure (space group C2) projected onto the (a) XZ, (b) XY, (c) YZ planes; Combination of the coordination polyhedra projected onto the (d) XZ, (e) XY, (f) YZ planes; Combination of selected coordination polyhedra projected onto the (g) XZ, (h) XY, (i) YZ planes; Coordination polyhedra for the (j) Ln1 and Ln2,(k) M1–M5,(l) B1–B7.

Crystals 2019, 9 FOR PEER REVIEW 25

The space group C2/c is known for the LnAl3(BO3)4 with the Ln = Pr, Nd, Sm, Eu, Tb, Ho (the structure is refined, for example, in [97]); LnFe3(BO3)4 with the Ln = Nd; LnCr3(BO3)4 with the Ln = La, Pr, Nd, Sm, Tb, Dy, Ho; LnSc3(BO3)4 with the Ln = La, Ce, Pr (Table 1). The centrosymmetry was determined by spectroscopic studies using a factor-group analysis of vibrations (for the LnAl3(BO3)4 with the Ln = Pr [42], Nd [42,45]; LnFe3(BO3)4 with the Ln = Nd [45]; LnCr3(BO3)4 with the Ln = La (Figure 10), Pr, Tb, Dy, Ho [70,71], Nd [26,45,70,71], Sm [70,72]). The LnSc3(BO3)4 crystals with the Ln = La, Ce, obtained by the Czochralski method, crystallize in the centrosymmetric space group C2 / c), according to a study of their nonlinear optical properties [35]. The XRD investigation of the CeSc3(BO3)4 microcrystal with the space group C2/c indicates the similarity of charge and as-grown Crystals 2019, 9, 100 22 of 49 crystal compositions [82].

I, a.u. Int.

8000 8e6

7e6

6000 6e6

5e6

4000 4e6

3e6

2000 2e6

1e6

10 15 20 25 30 35 40 45 50 10 20 2Theta30 40 50 2θ, deg

(a)

I, a.u. 7000

LSB 6000

5000

4000

3000

2000

1000

10 20 30 40 50 , deg

(b)

Figure 10. (a) Theoretical and (b) experimental diffraction patterns for the α - LaSc3(BO3)4 structure Figure 10. (a) Theoretical and (b) experimental diffraction patterns for the α - LaSc3(BO3)4 structure (space group C2/c). (space group C2/c). In the crystal structure with the space group C2/c (Figure7) the Ln atom is located at the center of aIn distorted the crystal trigonal structure prism with (CN the Lnspace=2 group + 2 + С 2)2/ (Figurec (Figure7j); 7) the the upper Ln atom triangular is located face at the of prism center is of rotateda distorted with trigonal respect prism to the ( lowerCN Ln one = 2 by+ 2 an + 2) angle (Figureϕ = 7j) 8◦;. the The upper Sc1 and triangular Sc2 atoms face are of prism located is in rotateddistorted with octahedra respect to (CN the Sc1 lower = 2 + one 2+ by 2, CNan angle Sc2 =  1 += 1 8°. + 1The + 1 Sc1 + 1 and+ 1) (FigureSc2 atoms7k), are and located the B1 and in B2 atoms are at the centers of scalene triangles (CN B1 = 1 + 1 + 1; CN B2 = 1 + 1 + 1) (Figure7l). A

comparison of crystal structures with the space groups R32 (Figure3) and C2/c (Figure7) shows their similarity (the same set of polyhedra; however, in the structure with the space group C2/c, there are two crystallochemically-different Sc atoms rather that one as in the structure with the space group R32) (Figure3g,h,I and Figure7j,k,l), on the one hand, and differences (the polyhedra in the structure with the space group C2/c are more distorted), on the other hand, i.e., the structure with the space group C2/c is more disordered compared to the R32. A similar alternation of layers of atoms ... Ln, Sc–B, O–Ln, Sc and Ln, Sc2–B, O–Sc1–B, O–Ln, Sc1, Sc2–B, O in the structures with the space groups Crystals 2019, 9, 100 23 of 49

R32 (XZ projection; Figure3b) and C2/c (XZ projection; Figure7a) and the corresponding polyhedra (Figure3d,f and Figure7d,g) should be mentioned. The low temperature phase γ-LaSc3(BO3)4 crystallizes in the space group Cc (a = 7.740(3), b = 9.864(2), c = 12.066(5) Å, β = 105.48(5)◦) (Figure8)[ 79], but there is no information on how its noncentrosymmetry was determined. The γ-LaSc3(BO3)4 single crystal was grown by the TSSG method from a flux and its structure was solved by direct method and refined by full-matrix least squares without any refinement of real crystal composition [79]. In the structure with the space group Cc (Figure8), which is positionally and structurally disordered compared with the α- LaSc3(BO3)4 modification with the space group C2/c (Figure7) the Sc1, Sc2, and Sc2 atoms are located in distorted octahedra (CN Sc = 1 + 1 + 1 + 1 + 1 + 1) (Figure8k), and the B1, B2, B3, and B4 atoms are at the centers of scalene triangles (CN B = 1 + 1 + 1) (Figure8l). According to Wang et al. [ 79], in the crystal structure of γ- LaSc3(BO3)4 (space group Cc), the La atoms are at the centers of distorted octahedra with the CN La = 1 + 1 + 1 + 1 + 1 + 1. However, according to the rotation angle ϕ = 14◦ between the upper and lower faces (Figure8j), which is larger than that in the structure with the space group C2/c (Figure7j), the La polyhedron is a trigonal prism, since it is nominally considered that a polyhedron with the CN = 6 is a distorted trigonal prism or a distorted octahedron in the angle ranges 0◦ < ϕ <<~ 30◦ or ~30◦ < ϕ < 60◦, respectively. Actually, based on a structure with the space group C2/c, the Sc2 crystallographic site (Figure7a–i) is ‘split’ into two sites, Sc2 and Sc3 (Figure8a–i), the B1 site (Figure7l) is ‘split’ into the B1 and B2 sites (Figure8l), and the B2 site (Figure7l) is ‘split’ into the B3 and B4 sites (Figure8l) with the formation of a structure with the space group Cc. Hence, a transition from the centrosymmetric structure with the space group C2/c to non-centrosymmetric structure with the space group Cc is obliged to ‘split’ sites (see, for example, Figures7f and8f). In the structures with the space groups C2/c and Cc, a similar alternation of layers of atoms and polyhedra with these atoms is observed on XZ projections: Ln, Sc2–B, O–Sc1–B, O–Ln, Sc1, Sc2–B, O (Figure7a,d) and Ln, Sc1, Sc2–B, O–Ln, Sc2, Sc3–B, O–Ln, Sc2, Sc3–B, O–Ln, Sc1, Sc3–B, O (Figure8a,d). Fedorova et al. [78], based on a complete correspondence (the space groups C2/c and Cc belong to the same diffraction symmetry group with the same extinction laws) of the diffraction patterns of powdered α-LaSc3(BO3)4 (space group C2/c) and γ- LaSc3(BO3)4 (space group Cc), obtained by solid ◦ state synthesis and heat-treated at temperatures from 1000 to 1350 C, concluded that the LaSc3(BO3)4 crystallizes in the space group C2/c. The experiment described does not allow choosing one of two space groups correctly. The unit cell parameters of single crystal grown from the charge having composition ◦ (Pr1.1Sc2.9)(BO3)4 (a = 7.7138(6), b = 9.8347(5), c = 12.032(2) Å, β = 105.38(7) )[83] are similar to ◦ those for the LaSc3(BO3)4 and CeSc3(BO3)4 (a = 7.7297(3), b = 9.8556(3), c = 12.0532(5)Å, β = 105.405(3) ) with the space group C2/c [82]. The extinction laws for the overwhelming number of diffraction reflections correspond to the space group C2/c or Cc (h + k = 2n for hkl, h = 2n, l = 2n for h0l, k = 2n for 0kl, h + k for hk0, h = 2n for h00, k = 2n for 0k0, l = 2n for 00l). Non-synchronous second harmonic generation was observed for these crystals, which indicates a non-centrosymmetric space structure Cc. A small amount of additional reflections with the I ≥ 3σ(I), typical for the space groups C2/m, C2 or Cm (h + k = 2n for hkl, h = 2n for h0l, k = 2n for 0kl, h + k for hk0, h = 2n for h00, k = 2n for 0k0), most likely, space group C2 as a subgroup of C2/c, is observed. The space group Cc was not found for the LnM3(BO3)4 with the M = Al, Fe, Cr, Ga. For the LnAl3(BO3)4 with the Ln = Pr, Nd, Eu, Gd, a modification with the space group C2 (a = 7.262(3), ◦ b = 9.315(3), c = 16.184(8)Å, β = 90.37 for the GdAl3(BO3)4)[47] was revealed. In the crystal structure of LnAl3(BO3)4 with the space group C2 (Figure9), five crystallochemically-different Al atoms are located at distorted octahedra (CN Al1, Al3, Al4, Al5 = 1 + 1 + 1 + 1 + 1 + 1, CN Al2 = 2 + 2 + 2) (Figure9k) and seven crystallochemically-different B atoms have a trigonal environment, two of which are isosceles triangles and the rest ones are scalene (Figure9l) [ 41]. The Ln (Gd) atoms occupy distorted trigonal prisms with the CN Ln1 = 1 + 1 + 1 + 1 + 1 + 1 and CN Ln2 = 2 + 2 + 2, and the rotation angle is ϕ ~ 20◦ (Figure9j), i.e., significantly higher than that for other modifications of huntite-like structures. Crystals 2019, 9 FOR PEER REVIEW 27

The space group Cc was not found for the LnМ3(BO3)4 with the M = Al, Fe, Cr, Ga. For the LnAl3(BO3)4 with the Ln = Pr, Nd, Eu, Gd, a modification with the space group C2 (a = 7.262(3), b = 9.315(3), c = 16.184(8)Å,  = 90.37 for the GdAl3(BO3)4) [47] was revealed. In the crystal structure of LnAl3(BO3)4 with the space group C2 (Figure 9), five crystallochemically-different Al atoms are located at distorted octahedra (CN Al1, Al3, Al4, Al5 = 1 + 1 + 1 + 1 + 1 + 1, CN Al2 = 2 + 2 + 2) (Figure 9k) and seven crystallochemically-different B atoms have a trigonal environment, two of which are isosceles triangles and the rest ones are scalene (Figure 9l) [41]. The Ln (Gd) atoms occupy distorted trigonal prisms with the CN Ln1 = 1 + 1 + 1 + 1 + 1 + 1 and CN Ln2 = 2 + 2 + 2, and the rotation angle is  ~ 20 (Figure 9j), i.e., significantly higher than that for other modifications of huntite-like structures. This feature of the LnAl3(BO3)4 crystal structure with the space group C2, which is the Crystals 2019, 9, 100 24 of 49 most disordered among all the huntite-like structures described (Figures 9a–i), does not exclude a tendency to reorganize a trigonal prism into an octahedron, accompanied by a decrease in the polyhedronThis feature volume of the Ln andAl3(BO degree3)4 crystal of its filling structure [98,9 with9]. It the may space be the group reasonC2, whichor one is of the the most reasons disordered for an absenceamong allof thethis huntite-like structure for structures the LnSc described3(BO3)4 compounds. (Figure9a–i), Nevertheless, does not exclude a comparison a tendency of to monoclinic reorganize compoundsa trigonal prism with into the anspace octahedron, groups C accompanied2/c (Figure 7), by Cc a decrease(Figures in8), the and polyhedron C2 (Figure volume 9) indicates and degree their identicalof its ﬁlling structural [98,99]. features: It may be ‘layers the reason’ of atoms or one and of polyhedra the reasons (Figures for an absence 7a and ofFigures this structure 7d, Figures for the8a andLnSc Figures3(BO3)4 compounds.8d, Figures Nevertheless,9a and Fgures a comparison9d), a connection of monoclinic of the compoundsLnO6 trigonal with prisms the space and groups ScO6 octahedraC2/c (Figure through7), Cc (Figurethe ВO83), triangles and C2 (Figure (Figures9) indicates 7g,h,i, Figures their identical 8g,h,i, Figures structural 9g, features:h,i). The ‘layers’ same structuralof atoms andfeatures polyhedra can also (Figure be observed7a,d, Figure for the8 a,d,compounds Figure9a,d), with athe connection space groups of the R32 LnO (Figure6 trigonal 3) and Pprisms321 (Figu andres ScO6 4–6). octahedra through the BO3 triangles (Figure7g–i, Figure8g–i, Figure9g–i). The same structuralBased featureson the experimental can also be observed data available for the to compounds date, it is possible with the to space limit groups the regionR32 (Figureof stability3) and of theP321 phases (Figures with4–6 ). the general composition LnM3(BO3)4, having the huntite-like structures, as a correlationBased onbetween the experimental the type of dataLn ion available and the to difference date, it is possible between to the limit ionic the radii region of of Ln stability and M of ions the (Figurephases with11). the general composition LnM3(BO3)4, having the huntite-like structures, as a correlation between the type of Ln ion and the difference between the ionic radii of Ln and M ions (Figure 11).

Al3+ 3+ Lu Fe Cr3+

Yb 3+ Tm Ga Er Sc3+ Ho Mg3+ (Y) Non-huntite family compound Dy

Tb Ln

Gd Eu Sm Nd Pr [Ca]

Ce La

0.150,15 0.200,20 0.250,25 0.300,30 0.350,35 0.400,40 0.450,45 0.500,50 (r VI - r VI), Å Ln M

Figure 11. The stability region for the phases with the general composition LnM3(BO3)4 with the M3+ = Al, Fe, Cr, Ga, Sc given as correlation between the type of Ln ion and the difference between the Figure 11. The stability region for the phases with the general composition LnM3(BO3)4 with the M3+ = ionic radii of Ln and M ions. Al, Fe, Cr, Ga, Sc given as correlation between the type of Ln ion and the difference between the ionic

radiiIn the of coordinatesLn and M ions. given in Figure 11, the huntite CaMg3(CO3)4 (space group R32) is located closer to the LnSc3(BO3)4, which may explain a formation of superstructures with full or partial ordering of atoms over the crystallographic sites (positional ordering) accompanied by a symmetry decrease in both CaCO3-MgCO3 and Ln2O3-Sc2O3-B2O3 system. In addition, there are other structural features of rare-earth scandium orthoborates. For polycrystalline and single-crystal samples with the general composition LnSc3(BO3)4, for VI VI which the rLn -rSc (Å) value is in the range of 0.285 (Ln = La) – 0.155 (Ln = Y) (i.e., with the minimum ∆rLn-M (Å) values among all the huntite-like structures) (Figure 11), a probability of obtaining compounds with the stoichiometric composition LnSc3(BO3)4 decreases, starting with the Ln = Nd (∆rNd-Sc = 0.235 Å). A distinctive feature of samples with the Ln = Sm (∆rSm-Sc = 0.215 Å), Eu (∆rEu-Sc = 0.215 Å), and Gd (∆rGd-Sc = 0.195 Å) should be a formation of internal solid solutions in the form (Ln,Sc)Sc3(BO3)4 (matrix ions are redistributed over different crystallographic sites resulting in a formation of antisite defects). In samples with the Ln from Tb (∆rTb-Sc = 0.175 Å) Crystals 2019, 9, 100 25 of 49

to Lu (∆rLu-Sc = 0.110 Å), internal solid solutions in the form (Ln,Sc)(Sc,Ln)3(BO3)4 will probably be formed. A formation of internal solid solutions can lead to a decrease in symmetry due to a positional Crystalsdisordering 2019, 9 FOR of thePEERLn REVIEWand Sc cations, which may ultimately results in the compounds going beyond 28 the limits of the stability region of the huntite-family phases (Figure 11). TheThe data data on on the the symmetry ofof compounds compounds with with the the general general composition compositionLnSc3 (BOLnSc3)43(BOare 3)4 are contradictory,contradictory, in in particular, particular, for for the the modifications modifications with with the space the space group groupR32. A R difficulty32. A difficulty of revealing of revealing the thespace space group groupP321, P321, which which was found was forfound the PSB for and the NSB PSB as aand result NSB of aas comparison a result theof experimentala comparison the experimentaldiffraction patternsdiffraction with patterns those given with in those databases given and in bydatabases the refinement and by of the crystal refinement structures of of crystal polycrystalline samples or powdered single crystals by the full-profile method (it is usually used in structures of polycrystalline samples or powdered single crystals by the full-profile method (it is practice), is associated with the almost complete similarity of theoretical diffraction patterns for the usually used in practice), is associated with the almost complete similarity of theoretical diffraction space groups R32 and R321 (Figure 12a,b). The differences relate only to the intensities of individual patternsreflections, for shownthe space in Figure groups 12a,b R in32 aand circle. R321 (Figures 12a,b). The differences relate only to the intensities of individual reflections, shown in Figures 12a and Figure 12b in a circle. I, a.u. nt.

8000

6000

4000

2000

10 15 20 25 30 35 40 45 50 10 20 30 40 50 2θ, deg

(a)

I, a.u. nt.

8000

6000

4000

2000

10 15 20 25 30 35 4040 45 5050 2θ, deg

(b)

Figure 12. Cont.

Crystals 2019, 9 FOR PEER REVIEW 29

Crystals 2019, 9 FOR PEER REVIEW 2θ, deg 29 (b) 2θ, deg

(b) Crystals 2019, 9, 100 I, a.u. 26 of 49 7000

PSB-1.1 6000I, a.u. 7000 5000 PSB-1.1 6000 4000 5000

3000 4000 2000

3000 1000 2000

0 1000 10 20 30 40 50 0 2θ, deg 10 20 30 40 50 2θ, deg (c)

NSB-1.0 6000I, a.u. 7000 5000 NSB-1.0 6000 4000 5000

3000 4000 2000

3000 1000

2000

0 1000 10 20 30 40 50 0 2θ, deg 10 20 30 40 50 2θ, deg (d)

Figure 12. Cont. (d)

Crystals 2019, 9 FOR PEER REVIEW 30

Crystals 2019, 9, 100 27 of 49

I, a.u.

7000

NSB-1.25 6000

5000

4000

3000

2000

1000

10 20 30 40 50 2θ, deg

(e)

Figure 12. Theoretical diffraction patterns for the (a) huntite structure (space group R32), Figure 12. Theoretical diffraction patterns for the (a) huntite structure (space group R32), (b) (b) superstructure of the huntite structure (space group P321), (c) structure with the space group P3121; 1 superstructureExperimental of the diffraction huntite patterns structure of powdered (space group single Р crystals321), ( (spacec) structure group P with321): (thec) Pr space1.1Sc2.9 group(BO3)4 P3 21; Experimental(PSB–1.1), diffraction (d) NdSc3(BO patterns3)4 (NSB–1.0), of powdered (e) Nd1.25 singleSc2.75(BO crystals3)4 (NSB–1.25). (space group Р321): (c) Pr1.1Sc2.9(BO3)4 (PSB–1.1), (d) NdSc3(BO3)4 (NSB–1.0), (e) Nd1.25Sc2.75(BO3)4 (NSB–1.25). Figure 12d–f show the experimental diffraction patterns of powdered PSB–1.1, NSB–1.0, and NSB–1.25 crystals with the space group P321, from which their similarity (with a certain redistribution Figures 12d–f show the experimental diffraction patterns of powdered PSB–1.1, NSB–1.0, and of the intensities of a series of reflections) and an analogy with the theoretical diffraction patterns NSB–1.25is also crystals seen. In orderwith tothe establish space the group space group,Р321, R32from and whichP321, in whichtheir thesimilarity rare-earth (with scandium a certain redistributionorthoborates of crystallize,the intensities it is necessary of a series to perform, of reflections) for example, aand single-crystal an analogy XRD experimentwith the theoretical with diffractionan analysis patterns of intensities is also seen. of reflections, In order as to was establish performed the for space the PSB group, and NSB R32 crystals and P [82321,]. in which the rare-earth scandium orthoborates crystallize, it is necessary to perform, for example, a single-crystal 3.2. Solid Solutions of Rare-Earth Scandium Borates XRD experiment with an analysis of intensities of reflections, as was performed for the PSB and NSB crystals [82].The symmetry of solid solutions in the LnSc3(BO3)4 – Ln’Sc3(BO3)4, LnSc3(BO3)4 – Ln’Sc3(BO3)4 – ScSc3(BO3)4 (space group R3c), LnSc3(BO3)4 – Ln’Sc3(BO3)4 – Ln”Sc3(BO3)4 systems is determined by 3.2. Solidthe Solutions space group of Rare-Earth and the ratio Scandium of the system Borates components. In the LaSc3(BO3)4-CeSc3(BO3)4 system, as well as in the LaSc3(BO3)4 – PrSc3(BO3)4 and CeSc3(BO3)4 – PrSc3(BO3)4 systems, provided that the ThePrSc symmetry3(BO3)4 crystallizes of solid in solutions the space groupin theC 2/LncSc, a3 formation(BO3)4 – Ln’ of aSc continuous3(BO3)4, Ln seriesSc3(BO of solid3)4 – solutionsLn’Sc3(BO3)4 – ScSc3(BOwith3)4 the(space space group group CR2/3c̅ c),should LnSc3(BO be expected.3)4 – Ln’Sc Limited3(BO3) solid4 – Ln” solutions,Sc3(BO3 which)4 systems can be basedis determined on the by compounds that actually exist, are formed in systems where the final members of solid solution the space group and the ratio of the system components. In the LaSc3(BO3)4-CeSc3(BO3)4 system, as belong to different symmetries (monoclinic and trigonal) (Figure 11). This obvious crystallochemical well as in the LaSc3(BO3)4 – PrSc3(BO3)4 and CeSc3(BO3)4 – PrSc3(BO3)4 systems, provided that the conclusion, based on the theory of isomorphic mixing, is confirmed experimentally (Table2). PrSc3(BO3)4 crystallizes in the space group C2 / c, a formation of a continuous series of solid solutions with the space group C2/c should be expected. Limited solid solutions, which can be based on the compounds that actually exist, are formed in systems where the final members of solid solution belong to different symmetries (monoclinic and trigonal) (Figure 11). This obvious crystallochemical conclusion, based on the theory of isomorphic mixing, is confirmed experimentally (Table 2).

Crystals 2019, 9, 100 28 of 49

Table 2. Summary structural data on solid solutions of rare-earth scandium borates.

Initial Composition Synthesis Method 1 Space Group Reﬁned Composition (Method) 2 Unit Cell Parameters, a, c,Å Reference

LaSc3(BO3)4-NdSc3(BO3)4 System

(La1−xNdx)Sc3(BO3)4 (x = 1.0) SSR and Flux R32 [25] R32 or C2/c (La Nd )Sc (BO ) (x ≤ 0.5) SSR and Flux [25] 1−x x 3 3 4 (depending on the crystallized temperature)

(La1−xNdx)Sc3(BO3)4 (x = 0.0–0.3) Czochralski C2/c [35,87]

(La1−xNdx)Sc3(BO3)4 (x ≥ 0.5) Czochralski R32 [100]

LaSc3(BO3)4-«GdSc3(BO3)4»System

LaxGd1−xSc3(BO3)4 (0.20 ≤ x ≤ 0.80) SSR R32 [101,102]

La1−xGdxSc3(BO3)4 (0.3 ≤ x ≤ 0.7) Flux R32 [88]

La1−xGdxSc3(BO3)4 (x ≥ 0.3) SSR R32 [103,104]

La0.6Gd0.4Sc3(BO3)4, TSSG R32 La0.77Gd0.22Sc3.01(BO3)4 [101]

La0.4Gd0.6Sc3(BO3)4, TSSG R32 La0.64Gd0.35Sc3.01(BO3)4 (ICP) [101]

La0.2Gd0.8Sc3(BO3)4 TSSG R32 La0.46Gd0.56Sc2.98(BO3)4 (ICP) [101] 9.7933 La Gd Sc (BO ) TSSG R32 La Gd Sc (BO ) (ICP) [101] x 1−x 3 3 4 0.78 0.22 3 3 4 7.9540 9.794(4) La Gd Sc (BO ) Czochralski R32 La Gd Sc (BO ) (ICP) [103] 0.678 0.572 2.75 3 4 0.64 0.41 2.95 3 4 7.961(6) 9.791 La Gd Sc (BO ) Czochralski R32 [104] 0.75 0.5 2.75 3 4 7.952

LaSc3(BO3)4-«YSc3(BO3)4»System

YxLayScz(BO3)4 (0.29 < x < 0.67, 0.67 < y < 0.82, SSR R32 [31,102,105] 2.64 < z < 3.00)

La0.77Y0.28Sc2.95(BO3)4, La0.76Y0.32Sc2.92(BO3)4, La0.80Y0.38Sc2.82(BO3)4, TSSG R32 [31,102,105] La0.73Y0.42Sc2.85(BO3)4, La0.75Y0.47Sc2.78(BO3)4 Y O :La O :Sc O :B O :Li O = 9.774(1) 2 3 2 3 2 3 2 3 2 TSSG R32 La Y Sc (BO ) (ICP) [31,102,105–107] 0.6:0.35:1.5:7:7.5 0.72 0.57 2.71 3 4 7.944(3) 9.805(3) Y La Sc (BO ) Flux R32 La Y Sc (BO ) (XRPD) [108] x 1−x z 3 4 0.75 0.25 3 3 4 7.980(2) 9.8185 La Y Sc (BO ) TSSG R32 La Y Sc (BO ) (ICP) [109] 0.72 0.57 2.71 3 4 0.826 0.334 2.84 3 4 7.9893 Crystals 2019, 9, 100 29 of 49

Table 2. Cont.

Initial Composition Synthesis Method 1 Space Group Reﬁned Composition (Method) 2 Unit Cell Parameters, a, c,Å Reference

LaSc3(BO3)4-«ErSc3(BO3)4»System LaEr Sc (BO ) 0.006 2.994 3 3.8 Czochralski C2/c [35] LaEr0.015Sc2.985(BO3)3.8

LaSc3(BO3)4-«YbSc3(BO3)4»System

LaYb0.15Sc2.85(BO3)3.8, LaYb0.3Sc2.7(BO3)3.8, Czochralski C2/c [35] LaYb0.36Sc2.64(BO3)3.8

LaSc3(BO3)4-«LuSc3(BO3)4»System

(Lu0.05La0.95)(Lu0.61Sc2.39)(BO3)4 ≡ 9.87420(10) LaxLuyScz(BO3)4 (x + y + z = 4) TSSG R32 [110] La0.95Lu0.66Sc2.39(BO3)4 (ICP) 8.0696(7)

LaSc3(BO3)4-«BiSc3(BO3)4»System

LaxBiyScz(BO3)4 (0.27 < x < 0.52 SSR R32 [111] 0.67 < y < 0.82 2.74 < z < 2.95) La O : Sc O : Bi O :B O =1 : 1.5 : 9.828(4) 2 3 2 3 2 3 2 3 Flux R32 La Bi Sc (BO ) (ICP) [111] 13 : 13 0.82 0.27 2.91 3 4 7.989(7) La O : Sc O : Bi O :B O = 9.8370(14) 2 3 2 3 2 3 2 3 Flux R32 La Bi Sc (BO ) (EDS) [112] 1 : 1.5 : 13 : 13 0.91 0.21 2.88 3 4 7.9860(14)

CeSc3(BO3)4-NdSc3(BO3)4System (Ce Nd )Sc (BO ) (XRD; P321 Ce Nd Sc (BO ) Czochralski P321 0.5 0.5(1) 3 3 4 [35] 0.53 0.64 2.83 3 4 3)

CeSc3(BO3)4-«GdSc3(BO3)4»System

(Ce0.7Gd0.3)Sc3(BO3)4 Czochralski P321 present work

(Ce0.485(3)Gd0.009Sc0.006))(Ce0.465(6)Gd0.017Sc0.018)Sc3(BO3)4 (XRD; P321 9.7812(10) (Ce0.8Gd0.2)Sc3(BO3)4 Czochralski P321 3 present work )(Ce0.803(2)Gd0.091(4)Sc0.106(4))Sc3(BO3)4 7.9480(12) (XRD; R32 3)

(Ce Gd Sc )Sc3(BO3)4 9.7776(42) Ce Gd Sc (BO ) Czochralski P321 0.949(1) 0.024(1) 0.027(1) present work 0.9 0.35 2.75 3 4 (XRD; R32 3) 7.9436(21)

CeSc3(BO3)4-«YSc3(BO3)4» System (Ce Y )Sc (BO ) (XRPD; R32 Ce Y Sc (BO ) Czochralski P321 0.78 0.22(2) 3 3 4 [35] 1.25 0.3 2.45 3 4 3)

(Ce Y Sc )Sc3(BO3)4 9.7553(25) Ce Y Sc (BO ) Czochralski P321 0.995(1) 0.002(1) 0.003(1) present work 1.25 0.3 2.45 3 4 (XRD; R32 3) 7.9680(12) Crystals 2019, 9, 100 30 of 49

Table 2. Cont.

Initial Composition Synthesis Method 1 Space Group Reﬁned Composition (Method) 2 Unit Cell Parameters, a, c,Å Reference

CeSc3(BO3)4-«LuSc3(BO3)4» System Ce(Lu Sc )(BO ) (XRPD; R32 Ce Lu Sc (BO ) Czochralski P321 0.17(1) 2.83 3 4 [35] 1.25 0.3 2.45 3 4 3)

Ce(Sc Lu0.090)(BO3)4 (XRD; 9.8085(21) Ce Lu Sc (BO ) Czochralski P321 2.910(30) present work 1.25 0.3 2.45 3 4 R32 3) 7.9829(10)

PrSc3(BO3)4-NdSc3(BO3)4»System

Pr0.99Nd0.11Sc2.9(BO3)4 Czochralski P321 [83]

PrSc3(BO3)4-«YSc3(BO3)4»System Pr Y Sc (BO ) (SEM/EDX) Nd O :Y O : Sc O : HBO : 0.94 0.09 2.97 3 4 2 3 2 3 2 3 2 (periphery part) 9.8256(5) 7.9038(4) Li (CO ) : LiF = TSSG R32 [113] 2 3 Pr Y Sc (BO ) (SEM/EDX) 9.8179(6) 7.9029(1) 0.25 : 0.25 : 0.8 : 2.75 : 0.177 : 0.246 0.93 0.10 2.96 3 4 (central part)

NdSc3(BO3)4-«GdSc3(BO3)4»System (Nd Gd )Sc (BO ) Nd Gd Sc (BO ) Czochralski P321 0.8 0.2(1) 3 3 4 [35] 1.125 0.125 2.75 3 4 (XRD; P321 3)

NdSc3(BO3)4-«YSc3(BO3)4»System Nd Y Sc (BO ) (SEM/EDX) Pr O :Y O : Sc O : HBO : Li (CO ) 0.86 0.21 2.93 3 4 2 3 2 3 2 3 2 2 3 (periphery part) 9.7588(5) 7.9186(9) : LiF = TSSG R32 [113] Nd Y Sc (BO ) (SEM/EDX) 9.7631(3)7.9210(7) 0.125 : 0.125 : 0.5 : 1.94 : 0.221 : 0.205 0.87 0.18 2.95 3 4 (part under the seed)

CeSc3(BO3)4-NdSc3(BO3)4-«GdSc3(BO3)4»System (Ce Nd Gd )Sc (BO ) (Ce Nd Gd )Sc (BO ) Czochralski P321 0.41(4) 0.46 0.13 3 3 4 [35] 0.65 0.25 0.10 3 3 4 (XRD; R32 3) (Ce Nd Gd )Sc (BO ) Ce Nd Gd Sc (BO ) Czochralski P321 0.57 0.25 0.18 3 3 4 [35] 0.76 0.30 0.14 2.8 3 4 (XRD; P321 3) Crystals 2019, 9, 100 31 of 49

Table 2. Cont.

Initial Composition Synthesis Method 1 Space Group Reﬁned Composition (Method) 2 Unit Cell Parameters, a, c,Å Reference

CeSc3(BO3)4-NdSc3(BO3)4-«LuSc3(BO3)4»System 21 reﬂections (space group R32): 9.776(6) 7.937(5) 18 reﬂections (space group A2): a0 = 7.895, Ce Nd Lu Sc (BO ) Czochralski P321 [35] 1.2 0.05 0.3 2.45 3 4 b0 = 9.749, c0 = 16.817, α = 90.23◦, β = 89.95◦, γ = 90.18◦

LaSc3(BO3)4-«ErSc3(BO3)4»-«YbSc3(BO3)4»System

LaYb0.15Er0.015Sc2.835(BO3)3.8, LaYb Er Sc (BO ) , 0.3 0.015 2.685 3 3.8 Czochralski C2/c [35] LaYb0.3Er0.003Sc2.67(BO3)3.8, LaYb0.36Er0.015Sc2.625(BO3)3.8 1 SSR—solid-state reaction; TSSG—top-seeded solution growth.2 ICP—inductively coupled plasma elemental analysis; XRPD—X-ray powder diffraction; EDS—energy dispersive spectra standardless analysis; XRD—X-ray (single-crystal) diffraction; SEM/EDX—scanning electron microscopy with energy dispersive X-ray spectroscopy. 3 A structure and composition were reﬁned in the space group speciﬁed. Crystals 2019, 9, 100 32 of 49

3.2.1. LaSc3(BO3)4-NdSc3(BO3)4 System

The XRD study of the (La1−xNdx)Sc3(BO3)4 (LNSB) solid solutions (x = 0.0–0.3) grown by the Czochralski method showed their crystallization in the space group C2/c [35,87]. The non-centrosymmetric trigonal phase R32 was discovered only in some crystals with high Nd3+ concentration (x ≥ 0.5) [100]. A trigonal symmetry was found only for NSB crystal (Ir seed). For LSB (Ir seed) as well as (Nd0.5La0.5)Sc3(BO3)4 and (Nd0.1La0.9)Sc3(BO3)4 with the LSB seed, a monoclinic symmetry was established. It confirms a role of a seed in symmetry of grown crystals. Symmetry of LNSB solid solutions (x = 0 to 1) obtained by the solid-state reaction and the flux method, was demonstrated by DTA, X-ray diffraction, second-harmonic generation, and fluorescence lifetime measurements [25]: for x = 1.0, i.e., for NdSc3(BO3)4, only trigonal phase existed, and for x ≤ 0.5, in the LNSB sample, two phases, with the space group R32 or C2/c, were obtained depended on the crystallized temperature (according to powder XRD, the phase with the space group R32 could be formed below 1100 ◦C). For the LSB (x = 0), the pure trigonal phase was difficult to obtain from the solid-state reaction. For example, in the LSB sample sintered at 1000 ◦C for 2 h, the huntite-family monoclinic phase and LaBO3 were found.

3.2.2. LaSc3(BO3)4 -«GdSc3(BO3)4» System

Polycrystalline LaxGd1−xSc3(BO3)4 (LGSB) solid solutions were obtained by the conventional solid-state reaction [101–104], and single-crystal ones were grown by the high-temperature TSSG method using the Li6B4O9–LiF as a flux [101,102] and Czochralski method [103,104] (Table2). A crystallization of polycrystalline samples in the space group R32 for 0.20 ≤ x ≤ 0.80 was established [101,102]. According to the XRD analysis, a single crystal grown by the high-temperature TSSG method crystallizes in the space group R32 and have the composition La0.78Gd0.22Sc3(BO3)4, refined using a full-matrix least-squares refinement on F2 (SHXLXL-97) using the occupancy factor for the La site fixed to a value that was determined from the ICP elemental analysis [101]. The composition of the single crystal grown by the Czochralski method from the charge La0.678Gd0.572Sc2.75(BO3)4 is determined by the inductively coupled plasma atomic emission spectrophotometry (ICP-AES) method to be La0.64Gd0.41Sc2.95(BO3)4 (space group R32) [103]. In addition, the LGSB single crystals were obtained by the Czochralski method from the charge with initial composition La0.75Gd0.5Sc2.75(BO3)4 without refinement of crystal real composition [104]. According to [101], as a result of investigation of polycrystalline LGSB samples, it was revealed that the stoichiometry of the single trigonal phase followed the relationship of Sc/(Gd + La) = 3 and the deviations from these values afford additional peaks of impurities in the X-ray powder diffraction patterns. Therefore, Gd occupies the La site rather than Sc site [100]. It is confirmed by the Gheorghe et al. [103]: according to the ICP-AES method, the stoichiometry of Sc is close to 3. According to [103,104], for polycrystalline La1−xGdxSc3(BO3)4 solid solutions, it was established that the structural changes from monoclinic (space group C2/c) to trigonal (space group R32) is complete for a Gd content larger than 0.3. The XRD investigation of a series of single crystal LGSB solid solutions, grown in 3:1 wt/wt LiBO2/La1−xGdxSc3(BO3)4 solvents or a 20 wt% CaF2 flux, showed that the R32 structural integrity is maintained for 0.3 ≤ x ≤ 0.7 [88].

3.2.3. LaSc3(BO3)4 -«YSc3(BO3)4» System

Polycrystalline and single-crystal LaxY1−xSc3(BO3)4 (LYSB) solid solutions were obtained by the solid-state reaction [31,102,105] and the high-temperature TSSG method using a lithium-borate flux [31,102,105–108], respectively (Table2). An investigation of phase equilibria in the LaBO3-ScBO3-YBO3 system [31,102,105] allowed to establish the limits of existence of huntite-type trigonal (space group R32) YxLayScz(BO3)4 solid solutions: 0.29 < x < 0.67, 0.67 < y < 0.82, and 2.64 < z < 3.00. Selected initial compositions of samples within the trigonal-huntite region of the phase diagram are given in [31,102,105] (Table2). The space group R32 has been determined for these Crystals 2019, 9, 100 33 of 49 samples by the powder XRD, and then was proven on the basis of the X-ray single-crystal refinement of structure of La0.72Y0.57Sc2.71(BO3)4. Occupancy factors for the La and Sc sites were fixed to the values that were determined by ICP elemental analysis, as deviations from these occupancies afforded increased residuals in the least-squares refinements. The solid solution with the trigonal symmetry, grown by the TSSG method, had an average composition La0.826Y0.334Sc2.84(BO3)4, determined by the ICP-AES [109]. According to the refinement of atomic coordinates and displacement parameters of LYSB structure of single crystal using a full-matrix least squares refinement on F2 (SHELXL-97) [31], its composition can be written as La0.72Y0.57Sc2.71(BO3)4 (space group R32), occupancy factors for the La, Y and Sc sites being fixed to the values determined by ICP-AES elemental analysis. Based on the comparison of cell volumes for the compositions La0.77Y0.28Sc2.95(BO3)4 and Y0.47La0.75Sc2.78(BO3)4 (La, Y, and Sc occupancies were determined by ICP-AES elemental analysis), in which the La concentrations 3 are similar, the higher Y concentration of La0.75Y0.47 Sc2.78(BO3)4 (V = 670.5(1) Å ) relative to that of 3 La0.77Y0.28Sc2.95(BO3)4 (V = 666.35(9) Å ) leads to a 0.6% increase in cell volume, which can only occur if the Y atom substitutes the small Sc site [31]. The structure of La0.75Y0.25Sc3(BO3)4 single crystal (space group R32) grown by the flux method was determined [108]. After full-matrix refinement with isotropic displacement coefficients on each atom, the occupancies of the La and Sc sites were refined. No significant change in the Sc occupancy factor was observed, so it was subsequently fixed to unity. Occupancy of the La site was significantly reduced, indicating occupation of Y on the La site. On the basis of the systematic condition −h + k + l = 3n for the hkil, the statistical analysis of the intensity distribution, packing considerations, and the successful solution and refinement of the structure, the crystal was found to form in the non-centrosymmetric space group R32.

3.2.4. LaSc3(BO3)4 -«ErSc3(BO3)4» System

Durmanov et al. [35] selected the optimal compositions of charge with a B2O3 deﬁciency, which prevents its deposition on the surface of the growing crystal, since liquid B2O3 drains into the high temperature region and dissolves the growing crystal. As a result, optically qualitative activated LaEr0.006Sc2.994(BO3)3.8 and LaEr0.015Sc2.985(BO3)3.8 crystals with the space group C2/c were obtained by the Czochralski method. Based on the crystallochemical similarity of Er with the Lu and Tb atoms, which, according to the XRD investigations, enter the Sc site [87], Durmanov et al. [35] suggested that the Er3+ ions also replace the Sc3+ ones. An increase in the concentration of Er3+ ions in the initial melt above 12 at % can lead to cracking of crystals and a change in their symmetry.

3.2.5. LaSc3(BO3)4 -«YbSc3(BO3)4» System

The optimal compositions of the charge with the lack of B2O3 to grow optically-qualitative crystals with the space group C2/c by the Czochralski method are LaYb0.15Sc2.85(BO3)3.8, LaYb0.3Sc2.7(BO3)3.8, 3+ LaYb0.36Sc2.64(BO3)3.8 [35]. Durmanov et al. [35] suggested that the Yb ions enter the Sc site based on the crystallochemical similarity of Yb with the Lu and Tb, which, according to the XRD investigations, occupy the Sc sites [87]. The maximum allowable concentration of Yb3+ ions to grow laser crystals is 10 at % (1.3 × 1021 cm−3); higher concentration cannot be achieved using the growth technology described in [35].

3.2.6. LaSc3(BO3)4 -«LuSc3(BO3)4» System

Polycrystalline and single-crystal solid solutions with the initial composition LaxLuyScz(BO3)4 (x + y + z = 4) were obtained by the solid-state reaction and the high-temperature TSSG method with a Li6B4O9 ﬂux [110], respectively (Table2). According to single-crystal XRD measurements, the solid solution having the composition La0.95Lu0.66Sc2.39(BO3)4, determined from the ICP elemental analysis, has been found to crystallize in the space group R32. Li et al. [110] suggested that the Lu atoms replace not only the La atoms in the trigonal prisms but also the Sc atoms in the octahedra; the formula for demonstrating Lu-atom substitution can be written as (Lu0.05La0.95)(Lu0.61Sc2.39)(BO3)4. Crystals 2019, 9, 100 34 of 49

3.2.7. LaSc3(BO3)4 -«BiSc3(BO3)4» System

Solid solutions with the general composition LaxBiyScz(BO3)4 were obtained in the form of polycrystals and single crystals using the solid-state reaction [111] and the spontaneous crystallization method using the Bi2O3–B2O3 as a flux [111,112], respectively (Table2). Xu et al. [ 111] established that the single trigonal phase covers the composition range of 0.27 < x < 0.52, 0.67 < y < 0.82, and 2.74 < z < 2.95. According to Xu et. al. [111], the Bi atoms replace not only the La atoms in the trigonal prisms but also the Sc atoms in the octahedra, and, hence, the general composition can be written as (La1−xBix)(BiySc3−y)(BO3)4. The unit-cell volume (V) varies with the sizes of both the trigonal prism and the octahedron, and it can be expressed in the equation by using atomic radii (R) and appropriately weighted occupancies for the Bi, La, and Sc atoms. Based on the equation given in [111], an approximately linear relationship between the effective concentration (Ceff ) and V was obtained, which indicates that the Bi atoms do indeed appear to be distributed across both sites. For the single crystal with the composition La0.82Bi0.27Sc2.91(BO3)4, determined from the ICP-AES elemental analysis, the space group R32 was found using the XRD analysis [111] (Table2). Single-crystal La0.91Bi0.21Sc2.88(BO3)4 solid solution, obtained by the spontaneous crystallization, the composition of which was checked with the energy dispersive spectra standardless analysis, has the trigonal structure with the space group R32, atomic sites and isotropic displacement factors being refined without any refinement of site occupancies [112] (Table2).

3.2.8. CeSc3(BO3)4-NdSc3(BO3)4 System

Single-crystal solid solution with the composition of the initial charge (Ce0.53Nd0.64Sc2.83)(BO3)4, grown by the Czochralski method, crystallizes in the space group P321 [35]. A comparison of the unit cell parameters, atomic coordinates, and interatomic distances of this phase with those for the NdSc3(BO3)4 allowed to receive the composition (Ce0.5Nd0.5(1))Sc3(BO3)4. The structure disordering of (Ce0.5Nd0.5(1))Sc3(BO3)4 is more pronounced compared with the NdSc3(BO3)4 [35].

3.2.9. CeSc3(BO3)4-«GdSc3(BO3)4» System Single-crystal solid solutions obtained by the Czochralski method from the charges having compositions (Ce0.8Gd0.2)Sc3(BO3)4, (Ce0.7Gd0.3)Sc3(BO3)4, and Ce0.9Gd0.35Sc2.75(BO3)4 crystallize in the space group P321 (Table2). According to the XRD analysis of microcrystals, 67% of diffraction reflections do not obey the extinction laws of the space group R32, but they are indexed in the space group P321, i.e., in the superstructure relative to the huntite structure. A refinement of the crystal structure of solid solutions with the nominal compositions (Ce0.80Gd0.20)Sc3(BO3)4 and Ce0.9Gd0.35Sc2.75(BO3)4 based on the strongest reflections (33%) in the subcell with the space group R32, i.e., in the huntite structure (atomic coordinates, atomic displacement parameters, occupancies of all crystallographic sites except for B and O ones), showed that their compositions can be described as (Ce0.803(2)Gd0.091(4)Sc0.106(4))Sc3(BO3)4 (R = 3.04 %) and (Ce0.949(1)Gd0.024(1)Sc0.027(1))Sc3(BO3)4 (R = 1.93 %), respectively. The refined crystal compositions correlate with the unit cell parameters (rCe>rGd>rSc), which are indicators of a composition. A refinement of the structure of the microcrystal with the nominal composition (Ce0.80Gd0.20)Sc3(BO3)4 in the space group P321 (i.e., taking into account all diffraction reflections, both strong and weak, but with the I ≥ 3σ(I); R = 3.13%) allowed writing the composition as (Ce0.485(3)Gd0.009Sc0.006))(Ce0.465(6)Gd0.017Sc0.018)Sc3(BO3)4 or (Ce0.950(3)Gd0.026Sc0.024)Sc3(BO3)4 (Tables3 and4). Crystals 2019, 9, 100 35 of 49

2 2 Table 3. Coordinates of atoms, atom displacement parameters (Beq × 10 ,Å ), and site occupancies (p) in the structure of (Ce0.80Gd0.20)Sc3(BO3)4 solid solution in the space group R32 and P321 according to the XRD data (AgKα).

Parameter Space Group R32 Space Group P321 Parameter Space Group R32 Space Group P321 Parameter Space Group R32 Space Group P321

−1 Z 3 µ, mm 3.90 3.87 θmax, deg 25.865 Reﬂ.: a,Å 9.781(1) 1765/591 1765/1765 wR 0.0500 0.0753 read/unique 2 c,Å 7.948(1) (I > 2σ(I)) R1 (I > 2σ(I)) 0.0304 0.0313 No. of V, Å3 658.53 37 90 S 0.857 0.978 parameters Site Ce1/Gd1/Sc Ce1/Gd1/Sc Site B2 Site O3 x 0 0 x 0.3282(4) x 0.3114(3) y 0 0 y 0.1146(5) y 0.2479(4) z 0 0 z 0.1705(5) z 0.1754(3) Beq 1.06(1) 1.11(1) Beq 1.28(6) Beq 1.96(8) p(Ce1/Gd1/Sc1) 0.1338(3)/0.0152(7)/0.0177(7) 0.1617(9)/0.0030(9)/0.0020(9) p 1.0 p 1.0 Site Ce2/Gd2/Sc Site B2 B3 Site O4 x 1/3 x 0 0 x 0.4755(4) y 2/3 y 0 0 y 0.1243(3) z 0.66638(4) z 0.5 0.5 z 0.1562(3) Beq 1.04(1) Beq 1.3(1) 1.4(2) Beq 1.56(5) p(Ce2/Gd2/Sc2) 0.155(2)/0.006(2)/0.006(2) p 0.16667 0.16667 p 1.0 Site Sc1 Sc1 Site B4 Site O2 O5 x 0.2141(1) 0.55053(9) x 2/3 x 0.58777 0.5989(5) y 1/3 0 y 1/3 y 0 0 z 1/3 0 z 0.8473(6) z 0.5 0.5 Beq 0.92(3) 0.92(2) Beq 0.82(9) Beq 2.4(1) 2.02(8) p 0.5 0.5 p 0.3333 p 0.5 0.5 Site Sc2 Site O1 Site O3 O6 x 0.21195(9) x 0.4560(3) x −0.1399(5) 0.1405(4) y 0.33235(6) y 0.1408(3) y 0 0.1405(4) z 0.32954(6) z 0.5228(3) z 0.5 0.5 Beq 0.86(2) Beq 1.44(5) Beq 1.54(8) 1.22(4) p 1.0 p 1.0 p 0.5 0.5 Site B1 B1 Site O1 O2 Site O7 x 0.4516(6) 0.4536(5) x 0.0193(4) 0.1930(4) x 0.6745(3) y 0 0 y 0.2116(4) −0.0209(3) y 0.1983(3) z 0.5 0.5 z 0.1813(4) 0.1769(3) z −0.1536(2) Beq 1.30(8) 1.05(8) Beq 1.58(6) 1.51(5) Beq 1.22(4) p 0.16667 0.5 p 1.0 1.0 p 1.0 Crystals 2019, 9, 100 36 of 49

Table 4. Main interatomic distances in the structure of of (Ce0.80Gd0.20)Sc3(BO3)4 solid solution in the space group R32 and P321 according to the XRD data (AgKα).

Parameter Space Group R32 Parameter Space Group P321 Ce1/Gd1/Sc Ce1/Gd1/Sc – 6 × O1 2.450(3) – 6 × O2 2.443(3) Ce2/Gd2/Sc – 3 × O4 2.417(3) – 3 × O1 2.484(3) [Ce2/Gd2/Sc-O]av. 2.4505 Sc1 Sc1 – 2 × O1 2.059(3) – 2 × O7 2.091(3) – 2 × O3 2.118(3) – 2 × O4 2.110(3) – 2 × O2 2.148(4) – 2 × O3 2.211(3) [Sc1-O]av. 2.129 [Sc1-O]av. 2.134 Sc2 – 1 × O2 2.035(3) – 1 × O1 2.041(3) – 1 × O5 2.113(3) – 1 × O3 2.124(3) – 1 × O6 2.129(2) – 1 × O7 2.149(2) [Sc2-O]av. 2.0985 B1 B1 – 1 × O2 1.33(1) – 2 × O1 1.378(4) – 2 × O1 1.368(5) – 1 × O5 1.412(8) 1.355 [B1-O]av. 1.389 B2 – 1 × O3 1.289(6) – 1 × O2 1.325(5) – 1 × O4 1.401(5) [B2-O]av. 1.338 B2 B3 – 3 × O3 1.369(5) – 3 × O6 1.375(4) B4 – 3 × O7 1.360(3)

3.2.10. CeSc3(BO3)4-«YSc3(BO3)4» System A refinement of the crystal structure of the Czochralski-grown powdered crystal with the initial composition Ce1.25Y0.3Sc2.45(BO3)4 by the Rietveld method in the huntite subcell with the space group R32 (the proper space group is P321: 67% of diffraction reflections do not obey the extinction laws of the space group R32) showed its real composition as (Ce0.78Y0.22(2))Sc3(BO3)4 [35]. A decrease in the Ce site occupancy was observed (the form factor or atomic factor is proportional to the atomic number), which indicates a partial replacement of the Ce atoms by the Y ones, and the presence of Sc atoms in this site has not been considered. The XRD analysis of the cation sites, except for the B site, in the structure of micropart of the same crystal (space group R32) resulted in the composition (Ce0.995(1)Y0.002(1)Sc0.003(1))Sc3(BO3)4 (R = 7.73 %), i.e., with the absence of Y atoms in the Sc site. Different compositions refined for powder and single-crystal samples can be explained by the heterogeneity of bulk crystal composition.

3.2.11. CeSc3(BO3)4-«LuSc3(BO3)4» System A reﬁnement of structure of the powdered sample in the space group R32 (the proper space group is P321) using the full-proﬁle method showed that the composition of the Czochralski-grown crystal Crystals 2019, 9, 100 37 of 49

can be written as Ce(Lu0.17(1)Sc2.83)(BO3)4 with a presence of the Lu ions in the octahedral sites of the structure together with the Sc ones [35]. The XRD analysis of the structure of micropart of the same crystal conﬁrmed the presence of Lu atoms in the octahedral site, but with a lower content: Ce(Sc2.910(30)Lu0.090)(BO3)4 (R = 5.95%).

3.2.12. PrSc3(BO3)4 -NdSc3(BO3)4 System

A solid solution with the charge composition (Pr0.99Nd0.11Sc2.9)(BO3)4 grown by the Czochralski method crystallizes in the space group P321 [83].

3.2.13. PrSc3(BO3)4-«YSc3(BO3)4» System

A solid solution with the general composition PrxYyScz(BO3)4 grown by the TSSG method using eutectic LiBO2–LiF as a flux crystallizes in the space group R32, as determined by the XRD on the powder sample [113] (Table2). According to scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM/EDX), a peripheral part of the crystal has the composition Pr0.94Y0.09Sc2.97(BO3)4, while the composition of the central part of the crystal is Pr0.93Y0.10Sc2.96(BO3)4 [113]. It should be noted that the unit cell parameters of samples from two parts of the crystal with almost identical compositions are signiﬁcantly different, although there is a tendency for the parameters to increase with increasing Pr content (rPr > rY) (Table2).

3.2.14. NdSc3(BO3)4-«GdSc3(BO3)4» System

The XRD analysis of the Czochralski-grown crystals with the initial compositions Nd1.125Gd0.125Sc2.75(BO3)4 (the reﬁned composition (Nd0.8Gd0.2(1))Sc3(BO3)4 was evaluated by comparing the structural parameters of this phase with those for the NdSc3(BO3)4), Nd1.04Gd0.26Sc2.7(BO3)4, and Nd0.91Gd0.39Sc2.7(BO3)4 showed their crystallization in the space group P321 [35].

3.2.15. NdSc3(BO3)4-«YSc3(BO3)4» System

Single-crystal solid solution with the charge composition NdxYyScz(BO3)4 was grown by the TSSG method [113]. The space group R32 was established by the powder XRD method. According to the SEM/EDX, a periphery part of the crystal has the composition Nd0.86Y0.21Sc2.93(BO3)4, while the region under the seed is Nd0.87Y0.18Sc2.95(BO3)4. A situation is similar to that found for solid solutions in the PrSc3(BO3)4-«YSc3(BO3)4» system: signiﬁcant differences in the unit cell parameters of samples taken from different parts of the crystal with almost identical compositions (taking into account a measurement error) are found, a noticeable correlation between the unit cell parameters and the Y content (rNd > rY) being observed.

3.2.16. CeSc3(BO3)4-NdSc3(BO3)4-«GdSc3(BO3)4» System The XRD study of a solid solution grown by the Czochralski method showed that its structure has the huntite subcell with the space group R32 (Table2). In this case, a limited number of weak diffraction reflections go into a superstructural trigonal cell with parameters doubled with respect to the huntite ones: A = 2aR32, C = 2cR32 [35]. The single-crystal XRD analysis of a solid solution with the charge composition Ce0.76Nd0.30Gd0.14Sc2.8(BO3)4 and estimated composition (Ce0.57Nd0.25Gd0.18)Sc3(BO3)4 revealed a significant number of superstructure reflections with the space group P321 [35]. Durmanov et al. [35] believe that the choice of the initial melt composition and growth conditions may rule out a formation of superstructure in the (Ce,Nd,Gd)Sc3(BO3)4 solid solution; among these compositions may be found a congruent melting one.

3.2.17. CeSc3(BO3)4-NdSc3(BO3)4-«LuSc3(BO3)4» System A large number of maximally-split reﬂections was revealed as a result of XRD investigation of a small chip of the Czochralski-grown crystal with the initial composition Ce1.2Nd0.05Lu0.3Sc2.45(BO3)4. Crystals 2019, 9, 100 38 of 49

The unit cell parameters determined by an auto-indexing the most intense 21 reflections correspond to the huntite cell with the parameters aR32 = 9.776(6), cR32 = 7.937(5) Å [35]. In the interval of interplanar distances d = 2.32–3.14 Å, weak and diffuse reflections, along with the strong ones, were found. The unit cell parameters determined from 18 reflections in the same interval of interplanar distances were found to be a0 = 7.895, b0 = 9.749, c0 = 16.817Å, α = 90.23◦, β = 89.95◦, γ = 90.18◦. The obtained triclinic unit cell is a pseudo-monoclinic one (space group A2) with the parameters correlated with those of the huntite 0 0 0 ◦ ◦ ◦ ◦ cell: a = cR32, b = bR32, c = 2aR32cos30 , α ~ 90 , β ~ 90 , γ ~ 90 . However, two weak (the intensities are 44 and 65 times less than the intensity of the strongest reflection in the above-mentioned interval) and diffuse (peak width are 1.56◦ and 2.73◦) reflections were not indexed with these parameters. Taking into account one weak (44 times weaker than the strongest reflection) and diffuse (width is 1.56◦) reflection, the a0 unit cell parameter doubles: a” = 2a0, b” = b0, c” = c0. However, the second reflection remained non-indexed with these parameters. A superstructure with the unit cell parameters a0, b0, c0 was also found for the solid solution with the composition (Ce0.80Gd0.20)Sc3(BO3)4 [84].

3.2.18. LaSc3(BO3)4-«ErSc3(BO3)4»-«YbSc3(BO3)4» System Durmanov et al. [35] selected the optimal compositions of the melt to obtain crystals by the Czochralski method (Table2). According to the XRD analysis, all grown crystals have a monoclinic symmetry, probably the space group C2/c. Based on the previous studies [76], Durmanov et al. [35] suggested that the Er3+ and Yb3+ ions replace the Sc3+ ones, and their maximum concentration in the initial melt should not exceed 12 at %, since a higher content may affect the cracking of crystals and change the symmetry (similar to solid solutions in the LaSc3(BO3)4 – «ErSc3(BO3)4» system). Thus, huntite-family solid solutions of rare-earth scandium borates crystallize either in a monoclinic symmetry with the centrosymmetric space group C2/c (in many works, the centrosymmetry is not confirmed) or in a trigonal one with the non-centrosymmetric space groups R32 (requires confirmation) or P321. In most cases, due to methodological difficulties of the XRD experiment, the site occupancies were not refined for the structures under investigation, especially when several cations with close atomic scattering factors occupy one crystallographic site. However, an elemental analysis and a crystallochemical approach made it possible to suggest the most likely composition from different compositions of solid solutions.

4. Crystallochemical Features of the Huntite Family The variety of compositions and different symmetries found for the huntite-family compounds and solid solutions allows to make their classification and systematization based on crystallochemical phenomena such as isomorphism (an ability of a system to form equivalents), morphotropy (a change in a crystal structure for a regular series of compounds having similar formula composition), polymorphism (an adaptability of a structure to external influences), and the adjacent polytypism (an ability of a substance to crystallize in various modifications with different packing of structural elements along one axis). Surely, there are no clear boundaries between them, but in the first approximation, this approach allows identifying general structural features and finding fundamental differences in the group of compounds or solid solutions. In addition to the possibility of forming continuous or limited solid solutions (the unlimited (perfect) and limited (imperfect) isomorphism) and internal ones (preferably for rare-earth scandium borates), a morphotropy is characteristic of the huntite-family compounds. The main reason for the morphotropy, in this case, is the size factor, namely, a change in the ionic radius of the Ln cation (LnAl3(BO3)4–LnGa3(BO3)4–LnSc3(BO3)4) (Figure1) or M cation (LaAl3(BO3)4–LaFe3(BO3)4–LaCr3(BO3)4–LaSc3(BO3)4, TbAl3(BO3)4–TbFe3(BO3)4–TbCr3(BO3)4– TbGa3(BO3)4–TbSc3(BO3)4, YbAl3(BO3)4–YbFe3(BO3)4–YbCr3(BO3)4–YbGa3(BO3)4) (Figure 11)[114]). The morphotropic series include nominally-pure and activated samples, for example, LaSc3(BO3)4 3+ (space group C2/c) – LaSc3(BO3)4:Cr (space group P1 or P1) (an electronic structure factor) [76] and 3+ LaSc3(BO3)4 (space group C2/c) – LaSc3(BO3)4:Nd (space group C2) (a size factor) [24]. Crystals 2019, 9 FOR PEER REVIEW 43

initial melt should not exceed 12 at %, since a higher content may affect the cracking of crystals and change the symmetry (similar to solid solutions in the LaSc3(BO3)4 – «ErSc3(BO3)4» system). Thus, huntite-family solid solutions of rare-earth scandium borates crystallize either in a monoclinic symmetry with the centrosymmetric space group C2/c (in many works, the centrosymmetry is not confirmed) or in a trigonal one with the non-centrosymmetric space groups R32 (requires confirmation) or P321. In most cases, due to methodological difficulties of the XRD experiment, the site occupancies were not refined for the structures under investigation, especially when several cations with close atomic scattering factors occupy one crystallographic site. However, an elemental analysis and a crystallochemical approach made it possible to suggest the most likely composition from different compositions of solid solutions.

4. Crystallochemical Features of the Huntite Family The variety of compositions and different symmetries found for the huntite-family compounds and solid solutions allows to make their classification and systematization based on crystallochemical phenomena such as isomorphism (an ability of a system to form equivalents), morphotropy (a change in a crystal structure for a regular series of compounds having similar formula composition), polymorphism (an adaptability of a structure to external influences), and the adjacent polytypism (an ability of a substance to crystallize in various modifications with different packing of structural elements along one axis). Surely, there are no clear boundaries between them, but in the first approximation, this approach allows identifying general structural features and finding fundamental differences in the group of compounds or solid solutions. In addition to the possibility of forming continuous or limited solid solutions (the unlimited (perfect) and limited (imperfect) isomorphism) and internal ones (preferably for rare-earth scandium borates), a morphotropy is characteristic of the huntite-family compounds. The main reason for the morphotropy, in this case, is the size factor, namely, a change in the ionic radius of the Ln cation (LnAl3(BO3)4–LnGa3(BO3)4–LnSc3(BO3)4) (Figure 1) or М cation (LaAl3(BO3)4–LaFe3(BO3)4–LaCr3(BO3)4–LaSc3(BO3)4, TbAl3(BO3)4–TbFe3(BO3)4–TbCr3(BO3)4–TbGa3(BO3)4–TbSc3(BO3)4, YbAl3(BO3)4–YbFe3(BO3)4–YbCr3(BO3)4–YbGa3(BO3)4) (Figure 11) [114]). The morphotropic series include nominally-pure and activated samples, for example, LаSc3(BO3)4 (space group C2/c) – Crystals 2019, 9, 100 39 of 49 LаSc3(BO3)4:Сr3+ (space group Р1 or P1) (an electronic structure factor) [76] and LаSc3(BO3)4 (space group C2/c) – LаSc3(BO3)4:Nd3+ (space group C2) (a size factor) [24]. TheThe polymorphicpolymorphic transition fromfrom the the space space group group PP31321121 to to the the R32R32 one one (from (from a low-symmetric a low-symmetric to a to ahigh-symmetric high-symmetric modificati modiﬁcation)on) with with increasing increasing temperature temperature is known is known for forthe theLnFeLn3(BOFe3(BO3)4 with3)4 with the Ln the Ln= Eu–Er,= Eu–Er, Y [53,56,57,58,60,62 Y [53,56–58,60,62,63-68]–68] (Figures (Figures1 and1, 13). 13 ).

Crystals 2019, 9 FOR PEER REVIEW 44 (a) (b)

(e) (f)

(g) (h) (i)

FigureFigure 13. 13. TheThe unit unit cell cell of ofthe the GdFe GdFe3(BO3(BO3)4 structure3)4 structure (space (space group group P3121)P 3projected121) projected onto the onto (a) theXY (a) XY andand (b ()b XZ) XZ planes; planes; Combination Combination of the of thecoordi coordinationnation polyhedra polyhedra projected projected onto the onto (c) the XY (andc) XY (d and) XZ (d) XZ planes;planes; Combination Combination of selected of selected coordination coordination polyhedra polyhedra projected projected onto the onto (e) the XY ( eand) XY (f) and XZ (planes;f) XZ planes; CoordinationCoordination polyhedra polyhedra for forthe the(g) (Gd,g) Gd, (h) Fe, (h) ( Fe,i) B1–B3. (i) B1–B3.

InIn the the LnLnFeFe3(BO3(BO3)4 3structure)4 structure with with the thelow-temperature low-temperature modification modiﬁcation (space (space group group P3121)P with3121) with thethe unit unit cell cell parameters parameters (Figures (Figure 13a,b) 13a,b) similar similar to those to those for the for huntite the huntite (space (space group group R32) (Ra 32)= 9.5305, (a = 9.5305, c = 7.5479 Å for the GdFe3(BO3)4), the polyhedra (Figures 13c-i) are the same as those in the structures c = 7.5479 Å for the GdFe3(BO3)4), the polyhedra (Figure 13c–i) are the same as those in the structures of ofhuntite-like huntite-like compounds: compounds: aa trigonaltrigonal prismprism for the Ln (Figure 13g),13g), an an octahedron octahedron for for the the Fe Fe (Figure (Figure 13h), 13h),and threeand trianglesthree triangles for the B atomsfor the (in theB huntiteatoms structure,(in the huntite there are structure, two crystallochemically-different there are two crystallochemically-different B atoms) (Figure 13i). A comparison of the XZ projections of the B atoms) (Figure 13i). A comparison of the XZ projections of the structures with the space groups R32 structures with the space groups R32 (Figure 3b) and P3121 (Figure 13b) shows a similar alternation (Figure3b) and P3 21 (Figure 13b) shows a similar alternation of atoms along the Z axis (Ln, Sc–B, of atoms along the Z 1axis (Ln, Sc–B, O–Ln, Sc–B, O) and polyhedra (Figures 3d, 3f and Figures 13d, 13f), but with corresponding gaps in the structure with the space group P3121 (compare Figure 3c and Figure 13c and Figure 3d and Figure 13d) due to the absence of the second helical axis. The space group P3121 was derived for the GdFe3(BO3)4 structure (90 K) from the systematic extinctions and was discriminated from other candidate space groups that comply with the same extinction conditions during the structure determination process; the polarity of the structure actually chosen (space group P3121) was determined by Flack’s x refinement [63]. Using circularly polarized X rays at the Dy L3 and Fe K absorption edges, Nakajima et al. [115] established that the single-crystal DyFe3(BO3)4, which has the chiral helix structure of Dy and Fe ions on the screw axes, belongs to the left-handed space group P3221, and this is in accord with the results on soft x-ray diffraction at Dy M5 absorption edge [116]. With an appropriate choice of the origin of the coordinates for the LnFe3(BO3)4 unit cell (on the Gd atom, Figure 13b), the topological similarity of the structures with the space groups R32 and

Crystals 2019, 9, 100 40 of 49

O–Ln, Sc–B, O) and polyhedra (Figure3d,f and Figure 13d,f), but with corresponding gaps in the structure with the space group P3121 (compare Figures3c and 13c and Figures3d and 13d) due to the absence of the second helical axis. The space group P3121 was derived for the GdFe3(BO3)4 structure (90 K) from the systematic extinctions and was discriminated from other candidate space groups that comply with the same extinction conditions during the structure determination process; the polarity of the structure actually chosen (space group P3121) was determined by Flack’s x refinement [63]. Using circularly polarized X rays at the Dy L3 and Fe K absorption edges, Nakajima et al. [115] established that the single-crystal DyFe3(BO3)4, which has the chiral helix structure of Dy and Fe ions on the screw axes, belongs to the left-handed space group P3221, and this is in accord with the results on soft x-ray diffraction at Dy M5 absorption edge [116]. With an appropriate choice of the origin of the coordinates for the LnFe3(BO3)4 unit cell (on the Gd atom, Figure 13b), the topological similarity of the structures with the space groups R32 and P3121 is observed. At the same time, the high-temperature modification is more symmetrical than the low-temperature one, which is typical of polymorphism [117]. For phases with the compositions (Ln,Sc)Sc3(BO3)4 and LnSc3(BO3)4, a polymorphic “order–disorder” phase transition (if the space group R32 is proven for these compounds) from the space group P321 (a disordered structure with a partial or full ordering of the Ln3+ and Sc3+ ions over two trigonal-prismatic sites and that of the Sc3+ ions over two octahedral sites) to the space group R32 (an ordered structure with a statistical arrangement of the Ln3+ and/or Sc3+ ions in one trigonal-prismatic site and that of the Sc3+ ions in one octahedral site) can be assumed with increasing temperature. On the other hand, it is possible that a kinetic ‘order–disorder’ phase transition (see, for example, [118,119]) occurs for rare-earth scandium orthoborates, i.e., a partially ordered phase (space group P321) is formed in the stability region of the disordered phase (space group R32) (a positional ‘ordering–disordering’) under an influence of kinetic (growth) factors. Growth dissymmetrization, as a rule, affects local parts of a crystal (hence, no more than 67 % of diffraction reflections, which did not correspond to the space group R32, were found), i.e., there is a different correlation between unit cells with different symmetries (a peculiar volume defect). A necessary condition for this kind of ordering in the structure is, first of all, the presence of sites jointly occupied by several crystallochemically-different atoms and their concentration. For example, an increase in the content of Yb activator in the scheelite-family (Na0.5Gd0.5)MoO4:Yb crystals grown by the Czochralski method leads to an increase in the degree of structure deviation from the space group I41/a and an increase in the orthorhombic distortion of the resulting superstructure [120]. For the (Na0.5Gd0.5)MoO4: 10% Yb crystals, ~50% of reflections, which are not inherent in the scheelite centrosymmetric space group I41/a, but typical for the non-centrosymmetric space group P4, was revealed by the XRD experiment [120]. It should be noted that only ~ 4% of such reflections was found for the (Na0.5Gd0.5)WO4: 10% Tm crystals (rGd > rTm > rYb), and (Na0.5Bi0.5)MoO4 crystallizes in the space group I4 [121]. An ordering depends on the growth method and synthesis conditions (for the Czochralski method: crystallization, cooling, and annealing rates; annealing and quenching temperatures; growth atmosphere, etc.). Indeed, an increase in growth rates from 4 to 6 mm/hour reduces a degree of structure ordering for the (Na0.5Gd0.5)WO4 crystal. The cooling rate of the crystals has a similar effect: a decrease in the cooling rate contributes to the formation of ordered non-centrosymmetric (Na0.5Gd0.5)WO4 and (Na0.5Gd0.5)WO4:Yb crystals (space group I4)[122]) Hence, a growth disymmetrization is most pronounced in conditions close to equilibrium. According to [46,123], for the LnAl3(BO3)4 compounds, a modification with the space group R32 is formed at low temperatures (~880–900 ◦C), phases with the centrosymmetric C2/c symmetry crystallize in the higher temperature region, up to 1040–1050 ◦C, and a further temperature increase leads to a formation of the most disordered and metastable non-centrosymmetric modification with the C2 symmetry. It can be seen that structurally disordered modifications with low symmetry are Crystals 2019, 9, 100 41 of 49 formed at elevated temperatures, which contradicts the rules of polymorphism, but it is characteristic of polytypism [124]. Inclusions of one polytype in another were revealed for the LnAl3(BO3)4 with the Ln = Nd and Gd by the IR spectroscopy using a factor group analysis for vibrations of the B–O bond [45]. Moreover, the structure of the monoclinic SmAl3(BO3)4 crystal contains significant fragments of the trigonal polytype, and the structure of the trigonal NdAl3(BO3)4 have a high content of domains of the monoclinic polytype. However, this conclusion was not confirmed by structural studies. The unit cell parameters of the huntite structure with the space group R32 (the hexagonal cell: aR32 = bR32 6= cR32) and those of the huntite-family structures are related as (Figure 14):

2 ◦ 2 1/2 2 ◦ 2 1/2 • aC2/c = 0.666[c R32 + (aR32cos30 ) ] , bC2/c = bR32, cC2/c = 0.666 [(2cR32) + (aR32cos30 ) ] (space group C2/c: a = 7.7297(3), b = 9.8556(3), c = 12.0532(5) Å, β = 105.405(3)◦)[82]; 2 ◦ 2 1/2 2 ◦ 2 1/2 • aC2/c = 0.666[c R32 + (aR32cos30 ) ] , bC2/c = bR32, cC2/c = [(2.5cR32) + (aR32cos30 ) ] (space group C2/c: a = 7.227(3), b = 9.315(3), c = 21.688(3) Å, β = 95.90(2)◦)[97]; Crystals 20192 , 9 FOR PEER REVIEW◦ 2 1/2 2 ◦ 2 1/2 46 • ac2 = 0.666[c R32 + (aR32cos30 ) ] , bc2 = bR32, c2 = 1.333[(1.25cR32) + (aR32cos30 ) ] (space group C2: a = 7.262(3), b = 9.315(3), c = 16.184(8) Å, β = 90.37◦)[47]. (space group C2: a = 7.262(3), b = 9.315(3), c = 16.184(8) Å,  = 90.37) [47]. It follows thatIt follows two unit that cell two parameters unit cell parameters are the same are for the the same huntite-like for the huntite structures,-like and structures, the third andc the third parameterc is parameter correlated is with correlat the othered with two. the other two.

<0001

CC2 CC2/c (c = 21.688(3) Å) CC2/c

CR32

<00 1 0 aR32cos30 Figure 14. GeneticFigure correlations14. Genetic correlations between the between unit cells the for unit the cells huntite for familythe huntite compounds. family compounds.

AccordingAccording to the results to the of theresults XRD of analysis the XRD of analysis the micropart of the micropart of the crystal of the with crystal the initial with the initial composition Nd Sc (BO ) (NSB–1.25), the unit cell parameters determined by auto-indexing of composition1.25 2.75 Nd1.253Sc4 2.75(BO3)4 (NSB–1.25), the unit cell parameters determined by auto-indexing of 21 reflections (h0h0, 000l) in the interval of interplanar distances d = 2.01–8.14 Å, correspond to the 21 reflections ( h0h0 , 000l) in the interval of interplanar distances d = 2.01 – 8.14 Å, correspond to the primitive trigonal cell with the cR32 parameter doubled with respect to the huntite one (a = aR32 = 9.74, primitive trigonal cell with the cR32 parameter doubled with respect to the huntite one (а = aR32 = 9.74, c = 2cR32 = 15.83 Å) [89]. In the interval of interplanar distances d = 3.96–4.00 Å, several diffuse с = 2сR32 = 15.83 Å) [89]. In the interval of interplanar distances d = 3.96 – 4.00 Å, several diffuse reflections with a width of 1.23–1.4◦ were found (the remaining reflections of approximately the reflections with a width of 1.23 – 1.4 were found (the remaining reflections of approximately the same intensity had a width of 1.05◦). Taking them into account (25 reflections), a primitive trigonal same intensity had a width of 1.05). Taking them into account (25 reflections), a primitive trigonal cell with the doubled aR32 and cR32 parameters (A = 2aR32 = 19.526(3), C = 2cR32 = 15.838(2) Å), as cell with the doubled аR32 and сR32 parameters (А = 2аR32= 19.526(3), С = 2сR32 = 15.838(2) Å), as for the for the (Ce0.41(4)Nd0.46Gd0.13)Sc3(BO3)4, was obtained. It should be noted that the refinement of the (Ce0.41(4)Nd0.46Gd0.13)Sc3(BO3)4, was obtained. It should be noted that the refinement of the NSB–1.25 NSB–1.25 composition in the space group R32 by the Rietveld method allowed to find its composition composition in the space group R32 by the Rietveld method allowed to find its composition as as NdSc3(BO3)4. An analysis of the atom displacement and positional parameters (first of all, for NdSc3(BO3)4. An analysis of the atom displacement and positional parameters (first of all, for the B2 atoms) indicates a structure different from the huntite with the space group R32. A similar diffraction picture was observed for the solid solutions in CeSc3(BO3)4 - NdSc3(BO3)4 - «GdSc3(BO3)4» and CeSc3(BO3)4 - NdSc3(BO3)4 - «LuSc3(BO3)4» systems. As a result of quenching of rare-earth aluminum orthoborates with the trigonal symmetry, in addition to the huntite-type modification (space group R32), a structural state with a full structural disorder in the alternation of layers along the c axis was revealed in the single-crystal diffraction patterns (diffuse bands on the reciprocal lattice along the с* parameter) [46]. In the diffraction patterns of monoclinic phases (space groups C2/c and С2), weak diffuse reflections, which should be absent due to extinction of space group reflections of the matrix structures, were also observed. All the above-mentioned experimental facts, namely, a presence of diffuse areas along with the point ones in the diffraction patterns, a presence of strong diffraction reflections with a high symmetry, the similar аR32 and bR32 parameters and the сR32 parameter, which can be represented as a linear combination of vectors (for classical polytypes, the similar а and b parameters and the c one multiple to minimum) meet the general principles of polytypism and are optimally described in terms of OD (order–disorder) theory [125].

Crystals 2019, 9, 100 42 of 49 the B2 atoms) indicates a structure different from the huntite with the space group R32. A similar diffraction picture was observed for the solid solutions in CeSc3(BO3)4 - NdSc3(BO3)4 - «GdSc3(BO3)4» and CeSc3(BO3)4 - NdSc3(BO3)4 - «LuSc3(BO3)4» systems. As a result of quenching of rare-earth aluminum orthoborates with the trigonal symmetry, in addition to the huntite-type modification (space group R32), a structural state with a full structural disorder in the alternation of layers along the c axis was revealed in the single-crystal diffraction patterns (diffuse bands on the reciprocal lattice along the c* parameter) [46]. In the diffraction patterns of monoclinic phases (space groups C2/c and C2), weak diffuse reflections, which should be absent due to extinction of space group reflections of the matrix structures, were also observed. All the above-mentioned experimental facts, namely, a presence of diffuse areas along with the point ones in the diffraction patterns, a presence of strong diffraction reflections with a high symmetry, the similar aR32 and bR32 parameters and the cR32 parameter, which can be represented as a linear combination of vectors (for classical polytypes, the similar a and b parameters and the c one multiple to minimum) meet the general principles of polytypism and are optimally described in terms of OD (order–disorder) theory [125]. The main factors for the formation of polytypes for the LnAl3(BO3)4 are a crystallization temperature (thermodynamic factor), a crystallization rate and a cooling rate in the flux method (kinetic factor), and a nature of the Ln cation and a rLn/rAl ratio (crystallochemical factor) [27]. For the LnAl3(BO3)4 with the Ln = Pr – Gd, two polytypic modifications with the space groups R32 and C2/c occur: for the Ln = Pr and Nd, a monoclinic structure is more stable; for the Ln = Sm, Eu, and Gd, a trigonal modification is more stable, a monoclinic phase is formed in the flux at high temperatures and concentrations only. In the case of orthoborates with the Ln = Tb - Lu and Y, a modification with the huntite structure is only stable [123]. Beregi et al. [97] concluded that the starting crystallization temperature is a dominant factor in formation of the trigonal and monoclinic symmetry: for the phase ◦ ◦ with the nominal composition Eu0.02Tb0.12Gd0.86Al3(BO3)4, a higher (1080 C) and lower (1060 C) starting temperatures led to an appearance of modifications with the space groups C2/c (a = 7.227(3), b = 9.315(3), c = 21.688(3) Å, β = 95.90(2)◦) and R32 (a = 9.294(2), c = 7.251(2) Å), respectively. Rare-earth scandium orthoborates, unlike other huntite-family rare-earth borates, exhibit a slightly different structural behavior. For example, for the LaSc3(BO3)4, three modifications are known: a low-temperature (space group Cc, is a subgroup of the space group C2/c and it is absent for other rare-earth orthoborates), a medium-temperature (space group R32; as was mentioned above, this group is denied by many researchers) and a high-temperature (space group C2/c) ones. The order of realization of the symmetry by the scandium borate crystals with increasing temperature is clearly different from that found for rare-earth aluminum borates: the most symmetrical structure crystallizes at high temperatures. It is quite possible that rare-earth scandium orthoborates are characterized primarily by polymorphs, although polytypes are also possible.

5. Conclusions A critical analysis of the data on growth and structural diagnostics (composition, structure) of the huntite-family compounds and solid solutions indicates the most complete and consistent data obtained for rare-earth aluminum orthoborates. Based on the results of investigation of the LnAl3(BO3)4 crystals with the Ln = Pr – Lu, Y obtained by the flux method (spontaneous crystallization and crystallization on a seed) with different solvents, a theory of polytypism is expanded (for example, [46]) due to the fact that all modifications known to date have been obtained and structurally characterized for aluminum orthoborates. The largest number of publications is devoted to activated and co-activated YAl3(BO3)4 crystals with the space group R32. Monoclinic modifications are referred less often, and their centrosymmetry or non-centrosymmetry was not proved but only stated for almost all rare-earth orthoborates. In addition, structural single-crystal studies for the LnCr3(BO3)4 having also a variety of modifications are absent to date, a symmetry being affected by the borate:solvent ratios in the batch during the spontaneous crystallization from a flux (Figure1). Crystals 2019, 9, 100 43 of 49

Crystal structures for almost all phases were determined (refined) using the X-ray experiment (there are several works on the neutron experiment, in particular [56,61,66–68]). The occupancies for the Ln and M sites were not refined (with a few exceptions), they often were fixed to those determined from the ICP elemental analysis. The real composition, obtained by refining the Ln and Sc site occupancies in structures of the LnSc3(BO3)4 crystals with trigonal and monoclinic symmetries, is generally not coincide and coincide with the charge composition, respectively. As a result, a congruent melting for the monoclinic phases is possible. Many questions remain to the rare-earth scandium orthoborates, since it is possible to find literature data with the opposite results on existence or absence of different modifications, in particular, a realization of the trigonal phases with the space group R32 or P321. This is primarily due to the fact that these phases are obtained by different methods under different conditions, and quite possibly, this modification can be obtained by a specific growth method under specific synthesis conditions. We failed to obtain the huntite-family LnSc3(BO3)4 compounds with the Ln = Sm and Gd by the solid-phase synthesis of the corresponding oxides at the T = 1000, 1250, 1500 ◦C and T = 1500 ◦C, respectively, although in the literature, there is data on the synthesis of the LnSc3(BO3)4 compounds with the Ln = Sm, Eu, Gd, Y. An X-ray study of single crystals with the nominal composition LnSc3(BO3)4 with the Ln = La, Ce, Pr, Nd, Tb and numerous solid solutions, grown by the Czochralski method, with the subsequent crystallochemical analysis of the results obtained, makes it possible to doubt the possibility of obtaining the LnSc3(BO3)4 with Ln = Sm, Gd, Eu, Y by this method. Although internal solid solutions with these components are possible to obtain by a careful selection of the initial charge compositions and synthesis conditions. When crystals are grown by the Czochralski method from melts at high temperatures, their symmetry depends on a composition and sintering temperature of a charge; a type, composition, symmetry, and orientation of a seed; a growth atmosphere, rotation, and pulling rates, as well as on an efficiently control both processes of B2O3 vapors condensation on the growing crystal and temperature gradients above the crucible and in the melt [35]. It should be noted that the LnSc3(BO3)4 can easy change its symmetry (group–subgroup), therefore a structural experiment should be performed on single-crystal objects with the analysis of diffraction reflections, including low-intensity ones (the use of high-resolution transmission electron microscopy and synchrotron radiation is also can be carried out), and the refinement of crystallographic site occupancies, i.e., real crystal composition. The refinement of structures by the full-profile method is correct only when using a developed methodology with criteria formulated to attribute the structure to the space group R32 or P321. This is important for establishing correlations between symmetry, real composition of objects and growth methods and conditions; correct explanation of functional properties observed; direct growth of crystals with a required combination of physical parameters, as well as for clarifying and summarizing crystallochemical data for the huntite family compounds and other functional materials.

6. Patents Kuz’micheva, G.M.; Podbel’sky, V.V.; Chuykin, N.K.; Kaurova, I.A. Program for the Investigation of the Dynamics of Changes in the Structural Parameters of Compounds with Different Symmetry; Certiﬁcate of state registration of computer software no. 2017619941: Moscow, Russia, 12 September 2017 (in Russian).

Author Contributions: Conceptualization, G.M.K.; Methodology, G.M.K. and V.B.R.; Software, V.V.P.; Validation, G.M.K., I.A.K. and V.B.R.; Formal Analysis, G.M.K., I.A.K. and V.B.R.; Investigation, G.M.K. and V.B.R.; Resources, G.M.K., I.A.K., V.B.R. and V.V.P.; Data Curation, G.M.K. and I.A.K.; Writing—Original Draft Preparation, G.M.K. and I.A.K.; Writing—Review & Editing, G.M.K.; Visualization, V.V.P.; Supervision, G.M.K. and I.A.K.; Project Administration, I.A.K. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest. Crystals 2019, 9, 100 44 of 49

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